US Senate negotiators remain short of an agreement as a year-end deadline looms to prevent tax increases for nearly all Americans.
President Barack Obama blamed Republicans for putting the shaky US economy at risk from the so-called fiscal cliff.
Senate Republican leader Mitch McConnell said he has asked vice president Joe Biden to become involved in a last-minute effort to reach an agreement. Senate majority leader Harry Reid acknowledged Mr McConnell made an offer last night but said "at this point we are unable to make a counter-offer".
The public exchange between the top negotiators on averting the fiscal cliff injected a note of pessimism little more than 24 hours before taxes are set to go up.
Democrats said Republicans were seeking to slow future cost of living increases for social security recipients as part of a compromise to avoid the impending tax hikes and across-the-board spending cuts.
Republicans declined to confirm the assertion - and one Republican official disputed it - but noted that Mr Obama said in a television interview broadcast earlier in the day that he had advanced such a proposal in earlier talks with Republicans.
The fate of the negotiations remained in doubt, with both the House of Representatives and Senate meeting during the day, two days before the beginning of a new year that would trigger across-the-board tax increases and spending cuts that leaders in both parties have said they want to avoid.
Democrats said the Republican proposal called for changing the formula for calculating social security benefits increases.
Mr McConnell said there is no single issue blocking an agreement but that "the sticking point appears to be a willingness, an interest, or courage to close the deal".
Mr Obama upped the pressure on Republicans to negotiate a fiscal deal, arguing that Republican leaders have rejected his past attempts to strike a bigger and more comprehensive bargain. He said: "The offers that I've made to them have been so fair that a lot of Democrats get mad at me."