That Cantor strongly backed the Speaker today doesn't mean that the corrosive dynamic can immediately be overcome. The reality is that a significant share of Republicans is probably not going to support a debt limit increase under virtually any circumstances. If, in the end, their instransigence is not met by some internal punishment e.g., concerning Committee assignments, the incentives for such intransigence could remain strong. Then, it is entirely plausible, that those holding the most extreme positions could exercise a sort of veto over Republican policy making. Such a situation would undermine Speaker Boehner's negotiating credibility and make it more difficult for the full House to forge bipartisan consensus. In turn, the absence of such consensus would promote further gridlock, leading to greater distrust among the two parties and growing frustration within each party.
IMO, it is imperative that the House Leadership make abundantly clear that Republicans must support the debt ceiling package on Wednesday and then any package that is reconciled with the Senate (the Senate version will differ) given the enormous stakes involved. Such a strong stand might be anti-democratic, but the consequences of a failure to raise the debt ceiling are sufficiently grave that Congressional leaders need to be willing to impose agreement, if necessary, to avert such an outcome. Occasionally, leaders need to take large risks and expend substantial political capital. This is one situation where such risktaking and expenditure of political capital is necessary.