Then Mr. Obama stopped backing up — and moved to generate momentum of his own.

The right’s soft spot, as Ronald Reagan and Newt Gingrich learned amid the conservative ascendancy of the 1980s and early ’90s, is the popularity of expensive “entitlements” serving the elderly.

“Cut spending,” as a general invocation, is popular. “Cut spending for your mother’s Medicare” is not.

Mr. Obama used his re-election campaign to isolate and attack that vulnerability. Acknowledging the need for some entitlement cuts, he offered voters this budgetary choice: his smaller cuts combined with tax increases on affluent Americans, or the Republicans’ bigger ones without tax increases.

More Americans, as polls have repeatedly shown, prefer Mr. Obama’s approach. He won the election.

Now the president is trying to wield his public opinion advantage as a club to back Republicans down.

The budget cuts of 2011, like sequestration now, targeted smaller “discretionary” programs that don’t command the support Medicare and Social Security do. Mr. Obama argues, and some Republicans agree, that Washington has cut most of what it can from those.

He continues to advocate comparatively modest Medicare cuts focused on reimbursements to doctors and hospitals — more near-term cuts, in fact, than Republicans have been willing to specify. But at one high-profile event after another, in Washington and across the country, he accuses Republicans of preferring reduced benefits for old and vulnerable Americans over higher taxes on the affluent.

Opponents blast him for “campaigning” instead of governing. Yet those events have become his method of seeking outcomes that negotiations with Republican leaders haven’t produced.