I don’t think the republicans are in a place where they can vote for any raise in the debt ceiling and not lose the tea bagger vote, or at least face a tea bagger in the primary.
Also keep in mind, if the talks fail to produce a deal that can pass, Republicans haven’t left themselves a back door. This remains a hostage situation — give the GOP the cuts it wants or they’ll block a debt-ceiling increase and create a recession on purpose. They’re no longer in a position in which they can say, “Well, we gave it a shot but the negotiations broke down. Let’s just go ahead and do the right thing now.”
I really don’t see anyway for republicans to get out of this without shooting the hostages, third world status here we come.