By Alan Fram and Andrew TaylorWASHINGTON -- The top Senate negotiators on the effort to prevent the government from going over the "fiscal cliff" offered a pessimistic assessment Sunday barely 24 hours before a deadline to avert tax hikes on virtually every worker. Senate Republican leader Mitch McConnell said he's yet to receive a response to an offer he made on Saturday evening to Majority Leader Harry Reid (D., Nev.), the top Democratic negotiator. The Kentucky Republican said he's reached out to Vice President Joe Biden in hopes of breaking the impasse, and a McConnell spokesman confirmed the two have spoken. Despite indications of progress in the negotiations, Democrats said Republicans were proposing to slow future cost of living increases for Social Security recipients as part of a compromise to avoid the cliff. Democrats rejected the idea. "I'm concerned with the lack of urgency here. There's far too much at stake," McConnell said. "There is no single issue that remains an impossible sticking point -- the sticking point appears to be a willingness, an interest or courage to close the deal." Reid said he has been trying to come up with a counteroffer but has been unable to do so. He said he's been in frequent contact with President Barack Obama, who in a televised interview blamed Republicans for putting the nation's shaky economy at risk. "We have been talking to the Republicans ever since the election was over," Obama said in the interview on NBC's "Meet the Press" that aired Sunday. "They have had trouble saying yes to a number of repeated offers." The pessimistic turn came as the House and Senate returned to the Capitol for a rare Sunday session. The fate of the negotiations remained in doubt, 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. Reid said he is not "overly optimistic but I am cautiously optimistic" but reiterated that any agreement would not include the less generous inflation adjustment for Social Security.