Senate Majority Leader Harry Reid said Sunday afternoon he has no further counteroffer to give his Republican counterpart as he and Minority Leader Mitch McConnell attempt to negotiate a plan to avoid the fiscal cliff.

McConnell — who said he has reached out to Vice President Joseph R. Biden Jr. to try to forge a last-ditch agreement — exchanged terse and matter-of-fact statements with Reid, D-Nev., on the Senate floor, casting doubt on the prospects for a deal that would prevent tax increases for all Americans beginning Jan. 1.

“I’ve had a number of conversations with the president, and at this stage, we’re not able to make a counteroffer,” Reid said at around 2 p.m. “The Republican leader has told me that … he’s working the vice president. … I wish them luck. In the meantime, I will continue to try to come up with something, but at this stage, I don’t have a counteroffer to make. Perhaps as the day wears on, I will be able to.”

McConnell, R-Ky., said he made his most recent offer around 7 p.m. Saturday, and that he had yet to receive a response from Democrats.

Later, Reid urged senators to remain prepared in case an agreement can be reached. “Everybody should hang loose. Something may break. And we’ll get something done,” Reid said.

Although Reid said he believed McConnell showed “good faith” over the weekend, some Democratic aides expressed exasperation over what they said were unanticipated GOP demands.

Senate Democratic aides said early Sunday afternoon that talks were falling apart as the GOP insisted on including the chained consumer price index, a way to adjust government benefits with inflation, in the current deal.

Democrats say chained CPI was only on the table as part of a larger agreement to get an extension of the expiring debt limit. But Republicans do not want the debt ceiling included in these negotiations, and so Democrats are balking at a request that would affect entitlement benefits for many Americans.

Democratic Sen. Chris Coons of Delaware said “there’s lots of different things” separating negotiators besides the chained CPI, but the provision that affects funds for Social Security hits at what many Democrats consider a core social program.

Republican sources would not confirm whether they are asking for the chained CPI and would only say that they were disinclined to discuss details of the ongoing talks and that the president has supported the measure. Democrats say they understood that there was a mutual understanding between the parties that the CPI would not be on the table if an increase in the government’s borrowing authority was also excluded from the negotiations.

An aide to Biden did not immediately respond to a request for comment on McConnell’s efforts to engage the vice president, and Capitol Hill sources outside of those two offices were unsure how those efforts might bear fruit.

“The vice president and I have worked together on solutions before, and I believe we can again,” McConnell said. “I want my colleagues to know that we’ll keep everyone updated. The consequences are too high for the American people to be engaged in a political messaging campaign. I’m interested in getting a result here.”

Sen. Kent Conrad, D-N.D., said he would not rule out voting for a package that included chained CPI. But he said “it would have to be part of a significant package.”

Alan K. Ota contributed to this report.