The latest rhetorical tool the President and his allies are using on John Boehner is telling him to put his money where his mouth is, specifically on the "clean" continuing resolution passed by the Senate. Boehner claims that if he allowed a clean CR to be voted on in the House, it would fail, so he must continue to demand a pound of flesh from the administration as the price of reopening the government. Barack Obama's response is, if that's true, then why not let it come up for a vote and see what happens? In recent days, a couple of news organizations have made counts of the Republican "moderates" (not all of whom are actually moderate) who have made public comments indicating they would support a clean CR. As of now, the Washington Post's tally has 21 Republicans in favor; combine them with the 200 Democrats, all of whom are likely to vote for the clean CR, and you've got a majority. But would these moderates actually follow through if it came to a vote?
As David Karol says in an excellent post on the topic of the moderates, "In general, Congressional moderates are more closely aligned to their parties than is understood. Often their defections from party ranks occur when it is clear that their party does not need their votes to prevail on a given issue." This is sometimes accomplished with a strategy that came to be known back when Tom DeLay was running things as "catch and release." The leadership makes sure it can win the vote, then slowly releases its moderates one at a time, allowing them to vote against the party so they can tout their independence but not threatening the outcome.
But that isn't the case here—there's a real question of which side would prevail. That means Republicans will be pressuring their moderates to stay in the fold. Karol also notes that even a Republican from a swing district could face a threat from a Tea Party challenger in a primary. Even if that challenger ends up losing the general election, if he beats you in the primary, you're still just as unemployed. So the question is whether the pressure on the moderates from within their party is greater or lesser than the pressure coming in the other direction.