The ghost of that narrative haunts the current moment, for as Obama heads into a similar dustup—those Bush tax cuts are again set to expire at the end of the year, just as automatic across-the-board budget cuts are scheduled to kick in, and another debt ceiling fight looms—members of the politirati (such as Yellin) are suggesting that Obama might once more turn tail and betray his promise to say no to another extension of these tax breaks for the rich.

But that narrative was wrong when it emerged—and it is not the key to predicting what Obama will do in the present predicament. Obama didn't wave the white flag in 2010. He turned a face-off over the Bush tax cuts into an opportunity to enact a second stimulus that he otherwise could not get past Senate Republicans. His failure at that time was not that he mustered insufficient mettle; he failed to convey to the world that he had jujitsued the GOPers.

For months prior to that tussle, the conventional view was accurate: The main issue was whether the tax cuts for the wealthy would continue. All the Bush tax cuts were due to evaporate at the end of 2010. (Bush had set that expiration date to diminish the tax cuts' impact on the long-term deficit.) During the 2008 campaign, Obama had promised not to raise taxes on middle-class earners and not to keep those Bush tax cuts for the top 2 percent. So he and his Democratic allies wanted to decouple the tax cuts for the rich from those for the rest—and extend only those for the bottom 98 percent.

Obama didn't surrender in 2010. He turned a face-off over the Bush tax cuts into an opportunity to enact a second stimulus that he otherwise could not get past Senate Republicans.

The Republicans balked at that notion. They contended this would amount to a tax increase—if only on those in the upper brackets. They threatened to block any move to continue only the tax breaks for the middle. And with the filibuster in the Senate, they were positioned to do so. Moreover, they signaled they would fiercely attack Democrats who voted to extend only some of the tax cuts as tax hikers (though these Democrats would merely be supporting a return to the rates of the Clinton years). A game of chicken was on. Obama and the Democrats claimed the Republicans were holding tax cuts for the middle class hostage. (No tax breaks for the rich, then no tax breaks for anyone else.) And the GOPers were daring Obama to stick to his position, see all the tax cuts perish, and end up being blamed for a rise in taxes for everyone.

There was solidarity on the GOP side, but not among the Democrats. In the summer of 2010, as the midterms approached, several Democratic Senate candidates told Senate Majority Leader Harry Reid and the White House they preferred not to vote on any legislation that would keep only the middle-class tax cuts alive. They feared the GOP effort to brand them tax raisers—which would be backed by unregulated special-interest campaign cash unleashed by the Supreme Court's Citizens United decision—would work. If there were a vote on decoupling the Bush taxes, White House aides figured, it was indeed possible that the president could not hold his side together.

In the White House, Obama and his aides gamed out various scenarios. With the economy sputtering in the second half of 2010, they worried that if the GOPers were hell bent on winning this game of chicken, taxes would go up for all at the start of 2011—as unemployment benefits were ending (for the Republicans were blocking an extension of those, as well)—and this would lead to a decrease in consumer demand that would roil the fragile economy. Lawrence Summers, the head of Obama's National Economic Council, fretted about a double-dip recession. Obama and his aides felt boxed in. The president had political promises to keep; he also had to prevent the economy from taking another downward turn.

In the fall of 2010—both before and after the midterm elections—Obama and his aides cooked up a different script. Fretting that the slow recovery was bottoming out, they had been searching for ways to juice up the economy. But they knew the notion of additional stimulus was a political nonstarter. Though Obama's original stimulus had worked, raising employment levels by millions of jobs (according to the nonpartisan Congressional Budget Office), Obama had lost that message war. The idea of government spending to boost the economy had become discredited. (See the tea party victories in the congressional elections.)

Obama's aides, though, also knew that by the end of the year there would be some legislation regarding the Bush tax cuts—however that knotty issue was to be resolved—and they came up with a plan to turn this measure into something of a Trojan horse that could contain (or hide) various stimulative measures. Before the midterm elections, Obama's economic team began compiling a list of possibilities, including a payroll tax cut and various tax credits.

At a postelection meeting with labor leaders and progressive activists, several of whom were itching for a tax cut fight with the Republicans, White House aides were blunt. To win these stimulative shots, Summers told them, we're going to have to give up on killing the tax cuts for the rich. "Getting more for our people is more important than getting less for their people," he said at the meeting.

Many House Democrats, though, were leaning on the White House to mount a battle royal. "We heard Democrats say, 'Let's make them vote over and over again on tax cuts for the rich,'" David Axelrod, a top Obama adviser, told me afterward. "'Go until January or February and people will know that's what the Republicans stand for.' We were flabbergasted. They missed the overall point that taxes would go up and unemployment insurance would be lost by 2 million. Obama was determined to get something done." Especially now that unemployment was near 10 percent and economic forecasts were worrisome.

Weeks after the election, as Democrats on the Hill and progressives in the trenches continued to urge Obama to engage in a shoot-out with the congressional Republicans over the tax breaks for the well-to-do, the White House began (secretly at first) negotiating a deal with Senate Republicans, with Vice President Joe Biden and Senate Minority Leader Mitch McConnell haggling. Obama was willing to eschew the fight his Democratic comrades yearned for in order to win something bigger and better: more stimulus to aid the ailing economy.

The president was also reluctant to see the game of chicken conclude with a crash that would result in taxes going up for the middle class and out-of-work Americans seeing the end to unemployment benefits. That could cause hardship for these Americans—and hinder the entire economy. And he, Biden, and others in the White House assumed that come the new year, the Republicans, with control of the House, would have an advantage. If Obama now stared down the GOPers and the Rs didn't blink, all the Bush tax cuts would disappear on December 31, 2010. Yet, presumably, the new Republican-controlled House would soon pass a bill extending all of the tax breaks. That legislation would move to the Senate, and the White House didn't trust Senate Democrats to hold the line against a measure cutting taxes for both the middle class and the high-end earners. So any major fight in December could well conclude with a Pyrrhic victory. Obama could stop the continuation of the tax breaks for millionaires, yet quite possibly only until the new Congress came to town—and there would be no new stimulus to boost the flagging economy.

There was another important factor affecting the president's thinking. Obama was looking to rack up other accomplishments during this lame-duck session, before the House would be in the hands of tea partiers. He was hoping to end the Pentagon's Don't Ask, Don't Tell policy, to ratify the New START nuclear arms reduction treaty, and pass the DREAM Act reforming immigration law. If he went DEFCON-1 on taxes with the Republicans, there would be no opportunity to steer these other measures through Congress in the holiday season, as it was wrapping up its business. It was quite clear: a bare-knuckles brawl on taxes would mean no more stimulus and no chance to abolish Don't Ask, Don't Tell, ratify that treaty, or pass any other legislation.

When the deal was done, many of Obama's own political allies did not immediately recognize what he had won. To many on the outside, it did seem as if he had caved.

So Obama went after a deal. And what Biden cooked up with McConnell was pretty good for the White House. The package would extend the Bush tax cuts for all taxpayers for two years and would reduce estate taxes for the wealthy (a move many Democrats couldn't stand), but it also included a payroll tax cut, a child tax credit, additional unemployment insurance, renewable energy grants, and other stimulative measures. A White House chart noted that Obama had won $238 billion of stimulus in return for yielding on $114 billion in high-income tax cuts.

In a way, Obama had sacrificed a stand of principle to push a second stimulus through Congress and provide a much-needed boost to the economy. It was a tough call. As I reported in my book, Showdown: The Inside Story of How Obama Battled the GOP To Set Up the 2012 Election, there were moments when Obama nearly walked away from the deal. But he succeeded in achieving his No. 1 priority: passing legislation that would produce economic assistance. The price, though, had been to yield to the Republicans on the upper-income tax breaks and the estate tax.

In policy terms, Obama clearly had gotten the better deal. The trouble was that the political world and the public had been conditioned to see this episode as primarily a clash over the top-tier tax cuts—and on that Obama had not gotten what he wanted. Consequently, the media depicted the compromise as a loss for Obama, and progressive Democrats squawked mightily about the continuation of the tax cuts. At a White House press conference following the deal's announcement, Ben Feller of the Associated Press challenged the president: "You've been telling the American people all along that you oppose extending the tax cuts for the wealthier Americans…So what I'm wondering is when you take a stand like you had, why should the American people believe that you're going to stick with it? Why should the American people believe that you're not going to flip-flop?" Moments later, Chuck Todd of NBC News noted that the Republicans had forced Obama "to capitulate."

This was not full capitulation. It was a strategic retreat to accomplish a bigger mission. Obama, however, never told this story. Throughout that lame-duck session, few in the media and few in Democratic congressional circles had realized what Obama was trying to pull off. When the deal was done, many of Obama's own political allies did not immediately recognize what he had won. To many on the outside, it did seem as if he had folded. As with the stimulus, the health care bill, and the middle-class tax cuts he had passed in his first year, Obama had neglected to convince the public of the value of his victory. And with 2010 coming to an end, and all eyes trained on the newly triumphant tea party, there was not much political space for this particular counternarrative. It didn't help that Summers, Axelrod, and other senior aides were not allowed to admit in public that the president had slyly achieved a second stimulus, for the S-word remained in disrepute.

Two years later, Obama still does not tell the story of that period well. In response to Yellin's question, he did not take explicit issue with her cave-in characterization:

Well, two years ago, the economy was in a different situation. We were still very much in the early parts of recovering from the worst economic crisis since the Great Depression. And ultimately, we came together not only to extend the Bush tax cuts, but also a wide range of policies that were going to be good for the economy at that point—unemployment insurance extensions, payroll tax extension—all of which made a difference, and is part of the reason why what we've seen now is 32 consecutive months of job growth and over 5.5 million jobs created and the unemployment rate coming down.

Yet Obama is right: the current circumstances are different, and after his reelection he is in a better position to do battle on the tax-cut front. He told Yellin:

[W]hat I said at the time is what I meant, which is this was a one-time proposition. And what I have told leaders privately as well as publicly is that we cannot afford to extend the Bush tax cuts for the wealthy. What we can do is make sure that middle-class taxes don’t go up.

In a recent White House meeting with labor leaders and progressive activists, Obama signaled he is ready to fight the GOPers—and this time dare the Republicans to block continuing the tax cuts for the middle class. But no one ought to forget that Obama, a progressive in his policy preferences, remains a pragmatist. What happened two years ago is not an indication that Obama is likely to yield in the new face-off, but that he will be assessing the political dynamics in gridlocked Washington and be willing to bargain hard for a good deal with true benefits. That's not caving in. It's governing.