There are at least 4 things I can think of that they can demand:
Repeal of Obamacare
Bush tax cuts made permanent
Balanced Budget Constitutional Amendment
Entitlement reform
Tell Obama he can have his debt increase but he has to agree to at least one of those.
Interesting list, only the last one is a nonstarter. They would promise, the GOP would give and then get nothing. The other three all could be passed at the same time in a single bill.
That is the only way the GOP members can deal with these people.