(ABC News)

Sen. Charles Schumer, D-N.Y., called Congress' failure to reach an agreement on a fiscal cliff deal "embarrassing," but said he believed there was a better than 50-50 chance of a compromise before taxes rise on a majority of Americans.

Schumer said Sunday on ABC News' "This Week" that he believes there is "a real possibility of a deal" in the final days before the New Year, as negotiations between Senate Majority Leader Harry Reid, D-Nev., and Senate Minority Leader Mitch McConnell, R- Ky., continued over the weekend.

Asked by ABC News' Chief White House Correspondent Jonathan Karl what the odds of a deal were, he said they were "a little better" than 50-50.

"On these big, big agreements, they almost all happen at the last minute," Schumer said. "So while an agreement is hardly a certainty, I certainly wouldn't rule it out."

Read the full transcript of Sunday's show HERE.

The Republicans' second highest ranking Senate member Sen. Jon Kyl, R-Ariz., agreed, emphasizing that not reaching an agreement would be "dire."

"If we are not able to reach an agreement, it will be dire," Kyl said. "And that's from everybody from the Congressional Budget Office… to the Fed chairman, probably at least another million jobs lost, an unemployment rate over 9 percent, and putting us back into recession."

"So responsible people on both sides of the aisle do need to try to come together, and there is a significant effort underway right now," Kyl added.

Schumer said it was "embarrassing" that a deal had yet to be reached with less than two days before the fiscal cliff, but said the Senate has shown signs of compromise.

"It is embarrassing, but almost every disagreement we've had is not because of the Senate where we've had lots of - you know, we've come to agreement on many things."

Schumer instead blamed House Republicans for resisting compromise on a final deal.

"There are 50 hard right people in the House who don't want to compromise. They don't believe in any revenues, they say compromise is a dirty word. And Speaker [John] Boehner just as recently as last week played their tune," Schumer said. "You cannot make a deal if you're going to let the people who are hardest right and uncompromising dictate what we should do."

But Kyl rejected Schumer's suggestion that House Republicans are to blame for the failure to get a deal.

"If the Democrats and Mr. Obama in particular don't get more seriously into that discussion, they have no standing to complain about the Republicans' lack of balance," Kyl said. "This is not just a problem with the House. The House passed legislation that would overt the fiscal cliff, both on the sequestration side and on the tax rate side. They've already acted."

Kyl said that Republican support for a deal would depend on President Obama's considering raising the level of income that would not face a tax increase beyond the current $250,000 level insisted on by the White House.

"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 [sic] a year," Kyl said.