The Opposition Opposes
I don't have a problem with Republicans who, on balance, wanted the bill to pass but still voted against it. I don't really think it's "cowardice" or whatever, they're simply making it clear that they're the opposition party. And that's a good thing! It's only in bizarro Broderville, combined with the annoying supermajority bits of the Senate, that anyone really thinks differently.
Basically, I agree. Both parties have an interest in differentiating themselves, and the best way to do that is to make the majority party responsible for its agenda.
But as Atrios also points out, there's one problem with this: "the annoying supermajority bits of the Senate." A parliamentary system is fine if you have the machinery of a parliamentary system, in which the majority party has the power to pass its legislative program and then stands or falls based on how well it works out. But it's not so fine if a party can win the presidency, the House, and the Senate by landslide majorities but still can't pass big parts of its program because it needs 60 votes in the Senate.
If Republicans want to adopt the party discipline features of a parliamentary system, fine. But they also need to adopt the rest of the system as well. The filibuster was never intended to become a routine requirement that all legislation needs 60% of the vote in the Senate to pass. But that's what it's become. It's time for reform.