I think the first use of the nuclear option should only be to fund the government with a CR though. Then the second time for the full funding. That should result in honest negotiations, even with Graham and McCain et al.
A couple impacts that the nuclear option might have are that it would seem to give a bit more power to the house, and Presidential Vetoes would be more numerous. But maybe that is what is needed.
The framers intended the power of the purse to be with the house (representatives of we the people).