Differences remained over details, including White House demands for middle- and low-income tax credits. But Republicans and Democrats appeared to come together Sunday, raising the possibility of a deal in Congress by the end of the week.
Some Democrats continued to object to extending current tax rates for high earners.
But without action, lawmakers face the prospect of delivering a tax hike to all taxpayers at the end of the year, when the current rates expire and revert to higher pre-2001 and 2003 levels.
Negotiations between the Obama administration and a bipartisan group of lawmakers centered on a two-year extension of current rates.
At the same time, a jump in the unemployment rate to 9.8 percent is putting pressure on Republicans to accede to President Barack Obama's demand that Congress extend unemployment insurance for a year. GOP congressional leaders had opposed an extension of benefits without cuts elsewhere in the federal budget.
"I think most folks believe the recipe would include at least an extension of unemployment benefits for those who are unemployed and an extension of all of the tax rates for all Americans for some period of time," said Sen. Jon Kyl of Arizona, the Senate's Republican negotiator in the talks, on CBS' "Face the Nation".
"Without unemployment benefits being extended, personally, this is a nonstarter," said Sen. Dick Durbin of Illinois, the second-ranking member of the Senate Democratic leadership.
Republicans have insisted that any extension of jobless aid be paid for with cuts elsewhere in the federal budget. The White House opposes that, saying such cuts are economically damaging during a weak recovery.
Sen. Orrin Hatch, R-Utah, said Republicans would probably cede that point to the Democrats.
"Let's take care of the unemployment compensation even if it isn't ... backed up by real finances," Hatch said. "We've got to do it. So let's do it. But that ought to be it."
About 2 million unemployed workers will run out of benefits this month if they are not renewed, and the administration estimates 7 million will be affected if the payments are not extended for a year.
Senate Republican leader Mitch McConnell on Sunday said discussions are still under way on a variety of unresolved issues.
The White House wants to include renewal of several other tax provisions that are expiring. These were initially included in the 2009 economic stimulus bill and include a tax credit for lower- and middle-class wage earners, even if they don't make enough to pay federal income taxes, breaks to offset college tuition and breaks for companies that hire the unemployed.
Any deal would require the approval of the House and Senate, and the president's signature. Mr. Obama told Democratic congressional leaders Saturday that he would oppose any extension of tax rates that did not include jobless benefits and other assistance his administration was seeking.
The short-term tax and spending debate is unfolding even as Congress and the Obama administration confront growing anxieties over the federal government's growing deficits.
A presidential commission studying the deficit identified austere measures last week to cut $4 trillion from the federal budget over the next decade.
The movement toward a possible compromise came after Republicans blocked Democratic efforts in the Senate Saturday to extend the current tax rates on all but the highest income levels. Republicans prefer extending all the tax rates permanently, but that cannot win legislative approval either. Even if it did, Mr. Obama would be sure to veto.
As part of a compromise, the Obama administration prefers a two-year extension of the tax rates. Officials say a one-year extension would place Congress and the president in the midst of a similar debate in a mere six months. A three-year extension, officials say, would cost too much and lose support from liberals.
The tax cuts will cost an estimated $65 billion a year, reports CBS News correspondent Nancy Cordes.
For Mr. Obama, the deal would mean relinquishing, at least for now, his long-held view that only middle-class voters should continue to benefit from Bush-era tax cuts. And Democrats, while resigned to a deal, were not eager to embrace one.
Durbin and Kyl spoke Sunday on CBS' "Face the Nation," while Hatch appeared on CNN's "State of the Union" and McConnell on NBC's "Meet the Press."