Because the Republicans are a minority in the Senate, because senators represent broader constituencies than congressmen, and because the structure of the upper chamber is designed to make compromise a necessity in any case, there’s a lot more room for Paul to be entrepreneurial on foreign policy (or for David Vitter to be entrepreneurial on banking reform, or for Marco Rubio to entrepreneurial — even if I think it’s in a mistaken cause — on immigration) than there is for a House leader charged with managing a fractious caucus to do the same.Yes, but. The problem here isn't so much House vs. Senate, or even leadership vs. rank-and-file (although that is a real consideration), but an absolute, self-imposed bright line against working with Democrats. Douthat says, correctly, that "the House runs on partisanship." And yet: it doesn't have to, at least not always. The mechanisms that allow the majority party to get its way whenever it is united are very real and important, but they do not, in fact, preclude cross-party majorities from potentially succeeding.
In fact, Douthat gives away the game: "obviously House Democrats aren’t about to go along with a measure designed as part of a larger strategy to pick apart Obamacare." Well, yes. If, however, Republicans were trying to improve health care...that's something that House Democrats, Senate Democrats, and Barack Obama might well go along with. So it's not being in the House that's the problem, and that's forcing Cantor to win almost every single Republican vote; it's that we're talking here about an explicitly partisan strategy, with the only question about whether Cantor's tactics are better than those of other House Republicans.
That's not what Paul is up to on foreign policy, or Vitter on banking, or Rubio on immigration. They're trying to get something substantive done (or, at least, get a reputation for trying to get something substantive done), and none of them are, apparently, terrified of being pictured with a Democrat. And, presto, they can find Democrats willing to work with them.
It's probably true that Eric Cantor can't follow that course if he also wants to be Speaker some day. But that's not inherent in the House, and it's even possible that Cantor (and Boehner, and other House leaders) might try to persuade the rank-and-file that there are real policy gains available through some sort of bipartisanship. Unfortunately, there's little sign that either Cantor or the House Republican conference in general are very interested in real policy gains. And that, and not anything else about the House, is why Cantor doesn't actually deserve much "credit for the effort."