Senate leaders hunkered down behind closed doors Saturday in search of a bipartisan blueprint for averting massive tax increases and spending cuts that will hit when the ball drops on New Year's Eve. The path forward, though, is lined with pitfalls that could sink any last-minute deal.

There was newfound optimism from the White House and congressional leaders as Senate Majority Leader Harry Reid, D-Nev., and Senate Minority Leader Mitch McConnell, R-Ky., began directly negotiating a plan that could swiftly pass both the Republican House and the Democratic Senate by Monday's deadline.

After months of ideological entrenchment on both sides, Reid and McConnell are scheduled to unveil a proposed deal on Sunday. Any plan would still have to weather the vastly different demands of Republicans, who are calling for deep spending cuts and entitlement reform, and Democrats, who want to raise the tax rate for wealthier Americans.

Reid and McConnell agree that taxes shouldn't go up on the middle class, but determining which Bush-era tax cuts should be extended remains the lawmakers' most pressing task.

Obama wants to cut taxes for families making less than $250,000 annually. Senate Republicans signaled they would agree to an extension for couples making less than $400,000 a year. But the House recently blocked a proposal that would have raised taxes solely on millionaires.

Still, some Republicans said Saturday that a deal was feasible, even under the tight deadline.

"We still can avoid going over the fiscal cliff if the president and the Democrat-controlled Senate step forward this week and work with Republicans to solve this problem and solve it now," Sen. Roy Blunt, R-Mo., said in the weekly GOP address.

Both sides agree that any possible deal would be little more than a stopgap measure that averts tax increases for all Americans. The most difficult parts of negotiations, spending cuts and changes to entitlements like Medicare, could be put off until after the New Year.

If lawmakers fail to reach a new agreement on what should be cut and by how much, across-the-board spending reductions will automatically kick in on Jan. 1 -- with half of the $1 trillion in cuts coming from the Pentagon.

House Speaker John Boehner, R-Ohio, said in a White House meeting Friday that any delay of the automatic cuts should be matched by fresh spending cuts. Democrats are likely to balk at that proposal.

Obama on Saturday again laid the responsibility on congressional Republicans for devising a deal that averts the cliff, though he also said that a compromise was possible.

"Congress can prevent it from happening, if they act now," he declared in his weekly radio address.

Obama will make his case again on NBC's "Meet the Press" on Sunday.

Reid is also planning to pin blame for a failure on the Republicans. If no deal is struck, Reid will call an 11th-hour Senate vote on a proposal that would raise the taxes of those making more than $250,000 a year, daring Republicans to vote against a middle-class tax cut.

Senate leaders did agree to one thing so far. They will put off talks on how to raise the government's borrowing limit and take up the debt-ceiling debate in coming weeks.