In principle, a debt ceiling bill could pass the US House of Representatives with something like 180 Democratic votes and 40 Republican votes. In that case, you wouldn’t need any tea partiers or even anyone with a safe GOP seat to vote for it. But the option isn’t being explored because it’s taken for granted that nothing will be moved to the floor of the House unless John Boehner signs off on it, and if Boehner were to green light a measure that the majority of his caucus disliked, he might be deposed. This is a “party cartel” dynamic. Powers that are formally assigned to the US House of Representatives are, instead, de facto exercised by the House Republican caucus and only measures that meet with the approval of the caucus can pass the House.
Except, as Jesse Richman writes (PDF) it hasn’t always had to work this way:
Describing his job in 2003, former Republican House Speaker Dennis Hastert asserted that “The job of the speaker is not to expedite legislation that runs counter to the wishes of the majority of his majority.” Cox and McCubbins’ (2005) first commandment for party leaders is consistent with Hastert’s claim: “Thou shalt not aid bills that will split thy party.” Further, Cox and McCubbins (p. 209) suggest that such negative agenda control is a constant in the US House of Representatives.
However, Hastert misunderstood the job of the speaker, and his mismanagement of the agenda contributed to the destruction of the majority he served. Former Democratic Speaker of the House Tip O’Neill described a more flexible approach to agenda control. In his autobiography, O’Neill recalled his reaction to the legislative agenda pursued by Ronald Reagan in 1981. “As Speaker, I could have refused to play ball with the Reagan administration by holding up the president’s legislation inthe Rules Committee. But in my view, this wasn’t a politically wise thing to do.” (O’Neill and Novak 1987, p. 344). O’Neill sacrificed agenda control in order to protect the Democratic majority. The majority was rolled (Cox and McCubbins 2005, p. 257) but the majority survived.
Richman’s thesis is that O’Neill had this right and strong carteling behavior has negative electoral consequences.