House Speaker John Boehner sent the White House a new proposal on ending the "fiscal cliff" showdown on Tuesday, in response to a fresh White House offer the day before, a senior Obama aide and a top Republican source said.
Obama and Boehner then spoke by telephone on Tuesday evening, the White House source said, though neither side divulged details of the plans, in line with a news blackout designed to guard any painfully won progress in the talks.
If no deal is agreed before the end of the year, taxes will go up on all Americans and automatic and savage cuts to government spending will begin, prompting fears the economy could dive into a new recession.
"We sent the White House a counter-offer that would achieve tax and entitlement reform to solve our looming debt crisis and create more American jobs," Boehner spokesman Michael Steel said.
"As the speaker said today, we're still waiting for the White House to identify what spending cuts the president is willing to make as part of the 'balanced approach' he promised the American people."
Signs that the bargaining process was becoming more serious came despite public sniping between the two sides on spending cuts earlier in the day, and warnings from both sides that time was running out.
Obama has demanded that Republicans agree to raise taxes on the rich as part of any deal, while Boehner has offered more revenue, but only by closing loopholes and capping deductions -- a plan the president says falls short.
"I'm pretty confident that Republicans would not hold middle class taxes hostage to trying to protect tax cuts for high-income individuals," Obama told ABC News.
"I don't think they'll do that."
Democrat Obama wants to extend George W. Bush-era tax cuts for 98 percent of taxpayers, but to allow rates on the top two percent to go up from 35 percent to 39.6 percent.
Republicans want to extend the tax cuts for everyone.
After days dueling over taxes, each side accused the other of failing to lay out specific spending cuts that both Republicans and Democrats agree are needed along with more revenue to cut around $4 trillion from the deficit.
"The longer the White House slow-walks this process, the closer our economy gets to the fiscal cliff," Boehner said.
"We're still waiting for the White House to identify what spending cuts the president is willing to make as part of the balanced approach that he promised the American people," he added before news of the fresh offers broke.
"Where are the president's spending cuts?" the House speaker asked, referring to Obama's original proposal to pare runaway debt by raising $1.6 trillion in new tax revenues.
Mitch McConnell, the top Senate Republican, made a similar charge, and then told reporters "we're running out of time."
Democratic Senate Majority Leader Harry Reid also said the clock was running down, warning that machinery of Congress meant that a deal was needed very soon, if lawmakers were to vote before the holiday season.
"The only thing standing in the way of an agreement is Republicans, their insistence on holding tax cuts for middle class families hostage," Reid said.
"I think it's going to be extremely difficult to get it done before Christmas, but it could be done."
White House spokesman Jay Carney insisted that Obama had laid out clear, detailed savings, in a deficit reduction document he sent to Congress in September 2011, and was sticking by the blueprint.
"The president, unlike any other party to these negotiations, has put forward detailed spending cuts as well as detailed revenue proposals," Carney said.
Obama and Boehner last met face-to-face on Sunday at the White House in a meeting described by both sides as "cordial."
It was also unclear whether Republicans decided to switch the conversation to spending as they thought they were losing the tax issue, as polls show a majority of Americans back Obama's call for tax hikes.