Republicans refuse to raise additional tax revenue, and until they do, Mr. Obama will not support even his own tentative proposals for reducing spending on fast-growing social benefit programs, chiefly Medicare. During a White House meeting with Senate Republicans on Friday, he reiterated that the two go hand in hand, according to people who were there.

“Revenue remains obviously the biggest stumbling block,” said Ed Lorenzen, executive director of the Moment of Truth Project. (The group is led by the chairmen of Mr. Obama’s failed 2010 fiscal commission, Erskine Bowles, a former chief of staff in President Bill Clinton’s administration, and Alan K. Simpson, a former Senate Republican leader from Wyoming.)…

Democrats and many Republicans also want to apply some new savings not to reduce the deficit, but to replace roughly $100 billion a year in across-the-board cuts known as sequestration, which since March have been hitting nearly all federal programs, including the military. Those cuts do not touch the benefit programs that are the root of the long-term debt problem.

While Republicans initiated the call for renewed negotiations, party lawmakers and senior aides said in interviews that they could not say what exactly Mr. Boehner would bring to the table. Some pointed to Mr. Ryan’s recent suggestions. By contrast, Mr. Obama’s plan is well known: over some Democrats’ objections, he put it in his annual budget in April, hoping his concessions would entice Republicans to parlay.