You mean the Heritage Foundation can force this to go past the debt ceiling deadline? Do they really have that much political influence?
In the Senate, probably not.
In the House, it remains to be seen. A crappy rating from them can be a death sentence for a member with a credible challenger, and its not like many of them are in districts where Democrats pose a threat.
Obviously it will be a myriad of factors. Democrat overreach (some of it intended I believe) and Boehner’s lack of clout.