The New York Times reports this morning that GOP Rep. Charlie Dent, a moderate from Pennsylvania, is working to round up House GOP support for allowing a “clean CR” funding the government, with no Obamacare defunding, to get a vote in the House. The GOP leadership still won’t say whether it will allow this in the end, because it would make conservatives very, very angry, but if this happened it would pass with a lot of Democrats — meaning no government shutdown.

Which raises a question: How many House Republicans would privately be okay with John Boehner allowing a clean CR to get a vote, even if they didn’t have to vote Yes on it?

In an interview with me today, Rep. Dent says he estimates over half of House Republicans could privately live with such a vote, even if it means the clean CR would end up passing with a lot of Democrats.

“There are a very large number of House Republicans who privately support a clean CR, but fewer who are willing to vote for it,” said Dent. “I believe most House Republican members would be okay with John Boehner if he were to decide to allow a vote.”

If he did, Dent continued, “it would pass with a strong bipartisan vote.”

This matters, because if a sizable enough bloc of Republicans would be okay with allowing a vote, then it becomes clearer Boehner is only holding out against allowing a vote because he’s continuing to placate a small conservative minority. It’s been widely assumed Boehner risks losing his Speakership if he allows such a vote, but Dent rejected that notion.

“Do I think this would compromise his Speakership? No, I believe John Boehner would still be secure,” Dent said. “Most members do not want the government to shut down, and the hourglass is nearly empty.” Dent, who said he prefers a CR that does defund or repeal parts of Obamacare, but recognizes it isn’t going to happen, described this group as follows: “Hope Yes, Vote No.”

“There are at least 180 or 190 members who are part of the governing wing of the House GOP conference,” Dent said. “There are just a few dozen who don’t have the same sense of governance.”

Dave Wasserman, who closely tracks House races and districts for the nonpartisan Cook Political Report, adds more. He notes some House Republicans don’t want to vote for a “clean CR,” because it might mean they face conservative wrath and even a primary, but would privately be okay with Boehner allowing a clean CR to get a vote, so a shutdown is averted for the good of the party.

Wasserman estimates that “probably slightly over half” would be okay with that. “These are fairly savvy seers of the national political mood,” Wasserman says. “Even while they’re fearful of a primary back home, they realize a government shutdown hurts their party’s brand. They just don’t want to defend a compromise vote back home.”

Wasserman characterizes this group as a combination of “true moderates” and “fairly conservative” members who are “not true believers.” Many of them, he says, are “mainstream conservatives” who are “not socially liberal but pay attention to what business leaders think.”

If it’s true that Boehner could allow this vote and still survive, why the last minute brinksmanship? One possibility, suggested by Robert Costa and Jonathan Strong, is that by taking us right up to the edge, and fighting until the last second for a CR that also chips away at Obamacare — only to have Senate Dems continue to reject it — Boehner can demonstrate to conservatives that this battle can’t be won, perhaps lessening the blowback if and when he does allow a vote on a “clean CR” that passes with a lot of Dems.

At any rate, Senate Dems are well aware of the possibility that Boehner can do this and survive as Speaker. They just released this new video illustrating the point: