For the first time, Senate Republicans describe to me the outlines of a possible deal: a package of immediate and specific budget cuts; budget caps reaching out five years to reassure conservatives that tough budget decisions will be made in the future; Medicare reforms short of the House approach; no tax increases — a Republican red line — but perhaps additional revenue from the elimination of tax expenditures.
The key conceptual breakthrough here seems to be Republicans agreeing to define the reduction of tax deductions as not constituting a tax increase. That's the point that Tom Coburn's fight with Grover Norquist was about.
A major part of the GOP's motivation seems to be protecting its members from the Paul Ryan plan to end Medicare:
Senate Minority Leader Mitch McConnell seems particularly intent on reaching a Medicare agreement different from Rep. Paul Ryan’s proposal. An incremental approach would allow Republican senators to say they confronted the problem, while allowing them to distance themselves from the unpopular House plan.