1. No legal significance
Sign-on letters are meaningless, legally speaking. And the number of signers is tiny for this kind of thing.

2. Legally false
There's no settled answer to what powers the president possesses in matters of war and peace. (See below.) Theoretically war can only be declared by Congress, but by precedent and law, they've clearly ceded enormous ground to the executive branch. The War Powers Act explicitly allows presidents to conduct a war for sixty days without congressional authorization. Moreover, Bill Clinton violated even this requirement during the 78-day Kosovo bombing campaign, with no consequences. It would be painful to listen to Hillary Clinton explain why he could do that but Bush can't attack Iran. (And if Bush does attack Iran, count on Republicans bringing up Kosovo over and over again.)

So if Bush decided to bomb Iran tomorrow, he would have an extremely strong legal case. But that doesn't matter anyway. Because:

3. War is purely a political question, and here the Webb letter might matter
I wrote about the general issue last spring in this Mother Jones article. The bottom line is if a president wants to attack another country, laws don't matter by themselves. He can do it if he's willing to pay the political price.

Imagine if Congress passed a law, over Bush's veto, prohibiting him from attacking Iran without further congressional authorization. If he still ordered the military to attack, high-ranking officers might resign. But eventually he'd find someone to do it. And off we'd go. Moreover Bush could rationally calculate that once the war started, Congress wouldn't have the balls to refuse to pass funding for it.

It's true such a law would have an enormous impact...but only because it would raise the political cost of war—causing more resignations, more Republican defections, and more angry editorials—rather than because it would make war "illegal." And here's the important point: Congress can raise the political cost without passing any new laws. See the Mother Jones article for some specific possibilities. But 22 Senators could make an enormous amount of noise if they were motivated and organized, particularly if they included presidential candidates.

It's here the letter might matter. It's unlikely the 22 Senators will end up causing too much trouble; note that (as far as I'm aware) there's been no coordination on this with outside groups. But the interesting thing about life is you truly never know.