“No matter the size of the cuts,” a House GOP aide says, “I have major doubts that any kind of revenue raises could pass the House.” Multiple Republican staffers suggest that Boehner faces as many, if not more, defections than the GOP did on the continuing resolution to keep the government running in April. Fifty-nine Republicans voted no on that deal; less than half of them were freshmen. Early on, Boehner called the debt-limit vote the first “adult moment” for the new GOP majority, but the Tea Party’s mantra has been that the vote represents their greatest point of leverage to force the kind of draconian cuts the conservative grassroots wants. The sentiment only deepened in the wake of the April budget deal. Some, like freshman Republican Jeff Landry, are ready to risk the dire consequences of default to make a point. “If I don’t get exactly what I want, I’m not voting for it,” Landry told Politico.

Faced with the prospect of losing up to 100 members, Boehner will have to assiduously court Democrats without exposing his right flank, particularly as Cantor, his No. 2, lurks over his shoulder. Democrats are laying down their own markers, vowing not to support a deal that includes cuts to benefits in entitlement programs like Medicare and Social Security, though several have expressed a willingness to discuss these cuts separately. “Because of the dogmatic, know-nothing wing that is willing to discard the interest of the country…at the altar of Norquist purism,” Connolly says, Boehner and Obama will ultimately find themselves needing a passel of Democrats to save a deal — likely more than the 81 Democrats who supported the CR in April. Connolly estimated some 100 Democrats would be required to thread the needle. “Triangulation isn’t going to work,” Connolly says. “You need the Democratic caucus to pass this. And so does John Boehner.”