The Senate's third-ranking Democrat said on Sunday that the odds of striking a deal to avert the "fiscal cliff" are a bit better than even, as he cautioned that there have been "no breakthroughs" yet in the talks between Senate Majority Leader Harry Reid (Nev.) and Minority Leader Mitch McConnell (Ky.).

"While an agreement is hardly a certainty, I wouldn't rule it out," Schumer said on ABC's "This Week With George Stephanopoulos." He pegged the odds of reaching a deal at "a little higher" than 50/50.

Sen. Jon Kyl of Arizona, the second-ranking Republican in the upper chamber, said he didn't disagree with Schumer's assessment. 

"If we are not able to reach an agreement, it will be dire," Kyl said on the same program.

Senate leaders worked through late Saturday to try to strike a deal and have set a 3 p.m. Sunday deadline for securing an agreement. 

Kyl said that if a majority of Republicans and Democrats in the Senate support a measure, it would stand a good chance of getting majority support in the House. 

"If there is enough in the agreement for Republicans to be able to support it and we can get a majority of Republicans in the Senate and a majority of Democrats in the Senate, then I think there's a good opportunity for a majority of Democrats and Republicans in the House to support such a package," said Kyl. "And I think a lot of that depends upon whether President Obama is willing to compromise this sort of fixation with raising taxes above anybody making more than $200,000 a year."