While leaders of both parties say they share the concern about the cuts, the proposals they continued to advance on Wednesday were far apart.
Aides said Democratic lawmakers had reached a consensus to join Obama in demanding more revenues as part of any deal.
Democrats believe that the American public backs that position. At a retreat in Annapolis, Maryland, they discussed new polling data showing that a strong majority of voters wants the wealthiest 2 percent of Americans - and large corporations - to pay more in taxes, even after the fiscal cliff deal raised tax rates on income above $450,000.
Republicans say that they have already given ground on more tax revenue, and any deficit reduction from here on out must come from spending cuts, a position repeated on Wednesday by Republican House of Representatives Speaker John Boehner.
In the U.S. Senate, a group of Republicans on the Armed Services Committee proposed delaying the spending cuts, known as a sequester, until the 2013 fiscal year ends on September 30.
But their plan would replace the $85 billion in cuts with savings achieved by shrinking the federal workforce by attrition over a multi-year period, an approach unacceptable to Democrats.
As government workers left their jobs, they would not be replaced. The plan also would extend a congressional pay freeze that was put in place as part of the January 1 fiscal cliff deal.
Those lawmakers said their plan would protect vital defense programs and military readiness.
“To my Republican colleagues ... if you feel comfortable with cutting the government this way, then you have lost your way as much as the president,” said Senator Lindsey Graham of South Carolina, issuing a challenge to those in his party willing to accept the cuts.