Update at 9:45 p.m. Deal Reached

Vice President Joe Biden was meeting late Monday with Senate Democrats to brief them on a proposed deal to stop sharp tax increases and spending cuts. A source told NPR the deal with congressional Democratic and Republican leaders includes a mix of both.

Senate Majority leader Harry Reid and House Minority Leader Nancy Pelosi have signed off on the agreement, which calls for a two-month deferral of the automatic spending cuts known as the sequester. The source says the cuts will be paid for half with revenue and half with more targeted spending cuts.

The Senate may vote on the deal Monday night, but there will be no vote in the House until Tuesday at the earliest.

Our original post:

Congress will not succeed in avoiding the "fiscal cliff" before New Year's Day, as the Senate isn't likely to vote on a potential deal until after midnight, and the House of Representatives has adjourned until Tuesday.

The failure comes after lawmakers and the White House spent weeks and months trying to work out a budget deal to avert tax hikes and budget cuts that will kick in automatically in 2013.

The House adjourned just before 6:30 p.m. ET; the chamber's next session will begin Tuesday at noon. A Senate vote on a deal could still come Monday night or early Tuesday. After meeting with other Republicans, Sen. Bob Corker (R-Tenn.) said he thinks "it's highly likely that some time this evening there'll be a vote on the Senate side," writes Ed O'Keefe of The Washington Post.

Corker said he and his fellow senators may vote on a deal after midnight.

"I think they're attempting to get the legislative language in order and vote on it tonight," he said, "you know, 1, 2, 3, 4 in the morning, whatever."

Any deal that is worked out would likely include terms that make it apply retroactively to the time between midnight tonight and the bill's enactment, NPR's Washington Editor Ron Elving tells us.

There are multiple news reports that the key provisions in the emerging deal include increases in income tax rates for families earning more than $450,000 a year and individuals who make more than $400,000. Other Americans' income tax rates would remain unchanged.

House members would want time to read any bill the Senate might offer, reports Reuters, citing "a Republican leadership aide." The aide also says a delay would have only a limited effect on the U.S. economy, as financial markets are closed Tuesday for the New Year's Day holiday.

As NPR's Washington Desk reminds us, legislators on Capitol Hill are also facing another deadline, and this one is beyond their control: At 11:59 p.m. ET Thursday, the 112th Congress will begin its final minute. Any budget crisis that lingers after midnight and into Friday would be the problem of the next Congress.

News that the New Year's Eve deadline might pass without Congress approving a deal follows comments by Senate Minority Leader Mitch McConnell earlier Monday that "we are very, very close" to reaching a deal.

President Obama said this afternoon that an agreement to prevent most Americans' taxes from rising at midnight is "within sight," but not yet done. An hour or so later, McConnell - the key Republican in talks about the so-called fiscal cliff - agreed.

As we've been reporting, there have been signs today of progress in the talks - which are now being led by Vice President Biden and McConnell. The so-called fiscal cliff is the midnight arrival of automatic tax increases, automatic spending cuts and the end of some unemployment benefits (all deadlines put in place by lawmakers back in 2011 during previous deficit-reduction and debt-ceiling negotiations).