WASHINGTON – Turning the newfound optimism for a deal to avoid the “fiscal cliff” into an actual deal will take 72 hours of deft political and procedural maneuvering through many of the same traps that have so far prevented an agreement.

Democrats and Republicans still have very different notions of who should pay higher taxes and who shouldn’t. And whatever party leaders come up with must still go through the thicket of politics in the slow-moving Senate and the anything-goes House.

“We’re trying to get the Rubik’s Cube all lined up,” Sen. John Barrasso, R-Wyo., said Friday evening.

The first step began Friday night, when senior aides to President Obama, Senate Majority Leader Harry Reid, D-Nev., and Senate Minority Leader Mitch McConnell, R-Ky., began negotiating pieces of a fiscal puzzle that must be fit together by the time the ball drops on New Year’s Eve.

Those talks are expected to continue Saturday, when both chambers of Congress will be shut down so Senate leaders can craft a deal that both of their caucuses are willing to accept.

Republicans have signaled a willingness to extend the George W. Bush-era tax cuts for all income up to $400,000, while Democrats prefer the $250,000 figure that Obama campaigned on.

Tied into that discussion was another over the estate tax, with Republicans and some western Democrats pushing to keep estates worth up to $5 million exempt from taxes, while Obama pushed to lower the threshold to $3.5 million.

Politically, the key is not just to pass something out of the Democratically controlled Senate, but also to do so with enough votes from Republicans to compel their House counterparts to support a deal. A bill with limited support from Senate Republicans would be dead on arrival in the GOP-dominated House, aides in both chambers said.

The critical deadline for the Senate-based negotiations is Sunday afternoon, according to Reid and McConnell. If they can come up with something by then, the Senate could approve it by late Sunday or late Monday morning, giving the House the rest of New Year’s Eve to consider it.

Even under this optimistic timeline, Senate and House leaders would need cooperation from the hard-liners in their respective caucuses, who could turn to procedure to block a compromise.

Under normal Senate rules, a new piece of legislation could take a full week to begin consideration, have full debate and then final passage. To avoid that, the Senate would instead likely take up a bill that has already passed the House and gut it and replace it with new language. Even so, McConnell would need to ensure that the most conservative Republicans don’t filibuster the measure or then force a lengthy 30-hour debate, which is allowed under Senate rules.

If all of that can be worked out, the Senate would ship a bipartisan deal across the Capitol Rotunda by Sunday night or Monday morning.

The first thing that would have to happen in the House is an agreement to waive a rule instituted under Speaker John Boehner, R-Ohio, that requires a full day between the time a bill is published and when it is voted on.

Boehner has also discussed amending a Senate-passed bill with a more conservative tilt on taxes. Amending the bill would send it back across the Senate for last-minute consideration, with many of the same procedural hurdles applying again and with the clock ticking steadily toward midnight.

Most congressional aides, however, have little faith in the speaker’s ability to amend anything, because Democrats would withhold their votes and he would need at least 217 Republicans to support him. That would set up a replay of Boehner’s ill-fated “Plan B” from last week, in which several dozen Republicans refused to support any increase in tax rates.

If there were not 217 GOP votes to amend the bill, Boehner would then hold a vote. And if enough Democrats and Republicans supported it and Obama were willing to sign it, Washington would have a deal.