I've said the best way for House Republicans to minimize the political damage of their Huge Mistake of voting for the Paul Ryan is to cut a deficit deal with President Obama. Yuval Levin agrees:

If Obama now makes a deal that involves some step, however small, toward transforming Medicare into a premium-support system, he would make a campaign of Medicare demagoguery far more difficult for the congressional Democrats, leaving them nothing to run on, unless they want to run against their own president.
But you can also see why this might appeal to both Obama and congressional Republicans. Even if the Medicare component of a debt-ceiling deal (a deal that would presumably also include serious discretionary cuts and statutory spending caps) was by no means a comprehensive reform, it could easily be enough for Republicans to try to run on building on a first step and for Obama to try to run on having done something to address the problem. More important, it offers each the prospect of taking some of the edge off of the other side’s chief political argument—the Republicans’ spending and debt crisis argument against Obama, and the Democrats’ Mediscare arguments against Republicans—while also actually doing something (however small) to begin to address the main driver of our fiscal problems.
The upside is probably larger for Republicans. If the economy remains in the doldrums, the party that, as DNC chair Debbie Wasserman Schultz said yesterday, “owns the economy” will be in very serious trouble, and having made some modest start toward a Medicare reform will not be enough to save the president. For the GOP, though, neutralizing the Democrats’ Medicare attacks while not taking Medicare reform off the table (indeed, while endorsing the key premise of the Republican reform proposals) would be immensely helpful.

Obviously I agree that Republicans would benefit from a deal that included Medicare. I'm not sure it would be "immensely helpful," though. The fact that Republicans voted to transform Medicare into coupons good for a discount off private insurance isn't the main problem. The main problem is that they voted to make those coupons radically and increasingly inadequate while also voting to cut taxes for the rich. That's an extremely unpopular policy tradeoff.

A Medicare deal wouldn't entirely or even mostly eliminate the liability. It would allow some moderate Republicans to edge away from the Ryan plan, by taking the view that they've solved the problem now and the radical plan they voted for will no longer be needed. That would help muddy the waters but it wouldn't completely shield them. Still, if I were a potentially vulnerable House Republican, I'd be looking for whatever cover I could get.