It remains unclear if a deal will happen before the end of the year or if the negotiations will carry over into 2013, after the fiscal cliff takes effect.
Without action now on the fiscal cliff, the nonpartisan Tax Policy Center estimates that middle-class families would pay about $2,000 a year more in taxes. Even with a deal, revisions in the tax code and other changes would mean everyone pays a bit more starting next year.
All signs point toward a two-step approach sought by Obama, with initial agreement now on some version of his tax plan with targets set for comprehensive negotiations on a broader deficit reduction deal in the new Congress next year.
Such an outcome would put off the main worry of the fiscal cliff, the expiration of the Bush-era tax cuts that would result in higher rates for everyone.
Obama and Democrats say they would then be ready to negotiate significant savings from entitlement programs, while Republicans say they need to first see commitment on entitlement reforms before accepting any higher tax rates.
McConnell, R-Kentucky, warned on the Senate floor on Tuesday that "until the president gets specific about cuts, nobody should trust Democrats to put a dime in new revenue toward real deficit reduction or to stop their shakedown of the taxpayers at the top 2%."
He and Boehner want Obama to take some of the political heat for proposing cuts to entitlement programs and other government spending.
On Tuesday, congressional Democrats rejected any cuts to the Medicaid health care system for poor and disabled Americans as part of a fiscal cliff deal. The opposition by Democrats showed the pressure Obama faces from his liberal base to avoid significant changes to the entitlement program that benefits millions.
Some in Congress warn that the legislative process will need at least a week to work through potentially complex measures from any proposed deal, meaning there is a de facto deadline of Christmas Day at the very latest for negotiators.
Retiring Sen. Kent Conrad, D-North Dakota, predicted Tuesday on MSNBC that a deal would get worked out in a week's time.
"It would be wise on their part not to come too quickly with a deal because that would give all the interest groups a chance to get organized and try to kill it," Conrad said. "And we know that on the right, on the left, special interest groups are just salivating at the chance to attack any agreement because, look, any agreement is going to have controversy attached to it."