But it was the inflation calculation that forced Democrats from the negotiating table. President Obama has said that in a “grand bargain” on deficit reduction, he would go along with the change, which would slow the growth of programs whose outlays rise with consumer prices, and would raise more revenue by pushing people into higher tax brackets.

Democrats said that Mr. Obama and Congressional Democrats would accept that change, called “chained C.P.I.,” only as part of a larger deal that included locking in well more than $1 trillion in revenue over 10 years, along with other Republican concessions. Democrats fear that any such concessions now would only increase demands for addition concessions in the coming weeks, when talks resume on a “grand bargain” to reduce the deficit.