Washington (CNN) - Senate leaders indicated Sunday that talks to avert the fiscal cliff have come to gridlock, as the upper chamber convened for a special session in hopes of passing a deal by the end-of-the-year deadline.
Republican Leader Mitch McConnell said on the Senate floor he has placed a call to Vice President Joe Biden to see if "he could help jump-start negotiations on his side."
Sources confirmed that McConnell and Biden have spoken twice.
A Democratic source familiar with the talks told CNN lawmakers have hit a "major setback" in the negotiations because Republicans are now insisting that any fiscal cliff deal include "chained CPI," which Democrats consider a "poison pill." Chained CPI would change the way Social Security benefits are adjusted for inflation, effectively meaning Social Security recipients would receive less money over the years.
READ MORE: Source: Fiscal cliff talks see major setback
McConnell said he submitted his latest proposal at 7 p.m. on Saturday.
"I'm interested in getting a result here," he said. "There's no single issue that remains an impossible sticking point. The sticking point appears to be willingness, an interest, or frankly the courage to close the deal. I want everyone to know I'm willing to get this done, but I need a dance partner."
Following his remarks, Senate Majority Leader Harry Reid spoke on the floor, saying he and his staff haven't been able to come up with a counterproposal.
"I had a conversation with the president and at this stage we're not able to make a counteroffer," Reid said.
As for McConnell's comments about working with Biden, Reid said, "I wish them well."
The majority leader added he will continue to work on another offer and will be able to make a new pitch "perhaps as the day wears on."
"I will say this: I think that the Republican leader has shown absolute good faith," Reid said. "It's just that we're apart on some pretty big issues."
– CNN's Dana Bash, Jessica Yellin And Ashley Killough contributed to this report.