President Obama’s budget today, as expected, recommends switching to chained CPI — a different calculation of inflation that would amount to a cut in Social Security benefits. And, as many expected, some Republicans are immediately attacking him for a “shocking attack on seniors.”

Regardless of its effect on negotiating position, and regardless of whether Democrats would be wise to accept a hypothetical deal involving chained CPI, the one thing that was fairly obvious was that putting it in the budget would produce Republican attacks. Even though Republicans had asked for entitlement cuts all along, the temptation for GOP politicians to reverse course and attack the very policy they asked for was inevitably going to be too great. And, as we’ve seen with Republican attacks on the Affordable Care Act’s Medicare cuts, which they supported, a little — or a lot — of inconsistency wasn’t going to get in the way.

What I wonder now, however, is whether Obama could salvage something of a win from all of this — at least assuming that his actual preference is to avoid Social Security cuts, and that, as he says, the inclusion of chained CPI is designed to show he’s open to compromise.

What if, assuming that Republicans continue to attack him for cutting Social Security, he simply withdraws the offer — and says that it is now clear that neither Republicans nor Democrats want to cut entitlements?

Yes, I know Republicans would immediately do their own double-back flip and attack Obama for not having a “serious” budget proposal since it would no longer contain the Social Security cuts they had just been attacking. And Obama would take a hit for it. But congressional Democrats would be off the hook, presumably … and perhaps Republicans would look even more foolish than the White House?

At any rate, if the reason to include chained CPI was to push Republicans to the bargaining table, there’s no reason at all for the White House to stick with chained CPI if the actual effect turns out to be the Republicans simply changing what Obama and the Democrats are being attacked for.