Key staffers huddle behind closed doors against the backdrop of a snowy capital as they attempt to hammer a last-minute deal to avoid going over the so-called fiscal cliff. NBC's Kristen Welker reports.

Updated 6:30 p.m. ET -- President Barack Obama tasked the United States Senate with trying to resolve the “fiscal cliff” in the waning hours before the New Year following a meeting between congressional leaders and the president.

Senate Majority Leader Harry Reid, D-Nev., and Minority Leader Mitch McConnell, R-Ky., will lead the last-minute effort to avert the automatic tax hikes and spending cuts set to take effect on Jan. 1 unless Congress acts.

And Obama said he is “optimistic” they can reach an accord before midnight on New Year’s Eve, the point at which the government would hit the fiscal cliff.

Absent that, the president said he had asked Reid to instead advance a bare-boned proposal that would extend the 2001 Bush tax cuts for income under $250,000.

Related -- Cliff Notes: Five things to watch at today's White House meeting

“I still want to get this done,” Obama said after his discussions with congressional leaders. He said “the hour for immediate action is here. It is now."

The president will appear exclusively on Sunday on NBC's "Meet the Press," where he's expected to further outline steps toward reaching a final deal.

The White House talks -- at which Obama presented no new offer to Republicans in Congress -- yielded “no concrete proposal,” Reid told reporters at the Capitol following the meeting.

President Barack Obama meets with NBC's David Gregory on Meet the Press Sunday morning. Gregory explains that for the president, this has become a matter of principle.

But in the waning hours before the end-of-year deadline, senators are now scrambling to produce a bipartisan package, at the request of Speaker John Boehner, R-Ohio, that can muster enough support in the House.

Reid, McConnell, Boehner, and House Minority Leader Nancy Pelosi, D-Calif., spent the meeting “discussing potential options and components for a plan that could pass both chambers of Congress,” according to a Boehner aide.

But the most significant development appeared to be the emerging consensus that any final agreement would have to emerge from the Senate. That deal would necessarily require a “bipartisan approach,” according to the office of McConnell, the Republican leader in the upper chamber.

Among the major sticking points, senior Democratic aides told NBC’s Kelly O’Donnell, involve the income threshold at which tax rates would be allowed to rise and the level at which estates are taxed.

Boehner’s failed effort last week to push through a fallback plan with only Republican votes laid bare the internal GOP divisions after conservatives balked at supporting a plan from the speaker to allow tax rates to rise on income over $1 million.

The unsuccessful effort suggested that Boehner would need to lean upon Pelosi for Democratic votes if a deal -- which has eluded Obama and Congress for the better part of the last two years -- is to pass.

A Senate-led agreement, though, faces no surefire guarantee of passage in the House.

“The speaker told the president that if the Senate amends the House-passed legislation and sends back a plan, the House will consider it -- either by accepting or amending,” Boehner’s aide emailed reporters.

One of the biggest sticking points in the fiscal cliff negotiations has been which income level ought to be required to pay additional taxes. On Friday, Democratic and Republican leaders met for an hour at the White House. NBC's Peter Alexander reports.

The protracted stalemate between Obama-led Democrats and congressional Republicans had prompted Friday's last-ditch meeting at the White House. It lasted just over an hour, and included Vice President Joe Biden and Treasury Secretary Tim Geithner.

Sources familiar with the meeting said that Obama made no new offer to Republicans, urging them to hold an up-or-down vote on a Democratic proposal to preserve existing tax rates for income under $250,000 and extend unemployment benefits (among other unresolved issues).

It’s that very proposal which Obama said he would ask Reid to advance should he and McConnell fail to strike a deal.

“I believe such a proposal could pass both houses with bipartisan majorities, as long as those leaders actually allow it to come to a vote,” he said.

Republicans had previously rejected such a proposal, but could feel pressure to relent to administration pressure in order to forestall across-the-board tax hikes in just a few days. The source familiar with the meeting told NBC's Peter Alexander and Kristen Welker that Obama asked Republicans what they would be willing to support, if not that proposal.

Amid negotiations toward a final deal, the House was set to return to Washington on Sunday at Boehner’s request, and remain at work through Jan. 2 -- the final day before the 112th Congress concludes and the next batch of lawmakers are sworn into office.

In the meanwhile, Obama voiced frustration toward the repeated pattern in Congress these past few years of lurching from crisis to crisis before reaching a last-minute deal to stave off catastrophe.

“The American people are watching what we do here. Obviously, their patience is already thin. This is deja vu all over again,” Obama said. “America wonders why, for some reason, in this town you can’t get stuff done in an organized timetable ... The American people are not going to have any patience for a politically self-inflicted wound to our economy.”