The differences over how to resolve the "fiscal cliff" narrowed significantly Monday night as President Barack Obama made a counter-offer to Republicans that included a major change in position on tax hikes for the wealthy, according to a source familiar with the talks.
The move, which the source stressed was not Obama's final offer, was welcomed, albeit with reservations, by a spokesman for Republican House of Representatives Speaker John Boehner, who met earlier in the day with Obama as the two hammered out a way to avert steep tax hikes and indiscriminate spending reductions set for the beginning of 2013.
(Read More: How Much Money Would Taxing the Rich Raise?)
In its most dramatic change in position yet, the White House proposed leaving lower tax rates in place for everyone except those earning $400,000 and above, a source familiar with the negotiations told CNBC. That's up from the $250,000 threshold the president has been demanding for months, but still far from Boehner's preference of $1 million.
The source said Obama has asked for a two-year boost in the debt ceiling with "periodic McConnell mechanism votes."
Obama also moved closer to Boehner on the proportion of a ten-year deficit reduction package that should come from increased revenue, as opposed to cuts in government spending.
Obama is now willing to accept a revenue figure of $1.2 trillion, down from his previous $1.4 trillion proposal.
Boehner's latest proposal calls for $1 trillion in new tax revenue, which would come from raising rates and limiting deductions that the wealthiest can take.
Some of the savings in spending proposed by Obama would come from reducing the size of cost-of-living increases for all but the most "vulnerable" recipients of the Social Security retirement program, the source said, through the use of a different formula to calculate the regular raises called "chained Consumer Price Index."
In the most hopeful sign, the source stressed that this was by no means the final offer from the White House.
The response from Boehner's spokesman was also a positive signal. "Any movement away from the unrealistic offers the president has made previously is a step in the right direction," the spokesman said, emphasizing that differences remain on spending levels in particular.
"We hope to continue discussions with the president so we can reach an agreement that is truly balanced and begins to solve our spending problem."
The rapid developments Monday evening put a deal realistically within reach.
The two men held talks at the White House earlier Monday and aides from both parties said they were optimistic an agreement was shaping up.
Though Obama and Boehner appeared to be edging closer to an agreement, substantial hurdles remain. Rank-and-file Republicans could have trouble with the tax increases on the wealthiest Americans that are likely to be part of any deal, while Obama could have a tough time selling spending cuts to his fellow Democrats.
But investors were cheered earlier Monday, before news broke of Obama's counter-offer, by signs of progress and the Standard & Poor's 500 index of U.S. stocks rose 1.19 percent.
(Read More: 'Fiscal Cliff' Talks Likely to Hold Markets Hostage)
Economists warn that going over the fiscal cliff could push the economy into recession.
Senate Democratic leader Harry Reid said his chamber will wrap up work on the issue after Christmas.
"It appears that we're going to be coming back the day after Christmas to complete work on the fiscal cliff," he said on the Senate floor.
Boehner faces a crucial test on Tuesday morning when he is expected to brief his party's lawmakers in the Republican-controlled House. He is not expected to bring any deal up for a vote unless a majority of the 241 House Republicans support it.
Republicans have campaigned for decades on a promise to keep taxes low, but Boehner in recent days has edged closer to Obama's demand to raise tax rates on top earners. In return, Obama could back a measure that would slow the rate of growth of Social Security benefits by changing the way they are measured against inflation, according to a Senate Democratic aide.
Getting Closer on Taxes
If there are no strong objections, he could try to finalize the deal with Obama on Wednesday, a Republican aide said.
Both sides declined to say what Boehner and Obama discussed at the meeting, which was also attended by Treasury Secretary Timothy Geithner.
The White House said Boehner's latest proposal does not meet its standards.
"Thus far, the president's proposal is the only proposal that we have seen that achieves the balance that is so necessary," White House spokesman Jay Carney said at a news briefing.
Republicans understand that the clock is ticking and they are confident that Boehner will get a deal they can support in the coming days, a senior House Republican aide said.
Republicans want substantial spending cuts in return for increased tax revenue, but any proposal to trim popular benefit programs like the Medicare health insurance plan for seniors will face fierce resistance from liberal Democrats, whose votes will be needed to get a deal passed.
Obama could also face strong opposition from Democrats if he agrees to Boehner's proposal to slow the growth of Social Security benefits by changing the way the cost-of-living increases are measured against inflation, an approach that could save $200 billion over 10 years.
)Obama also wants to head off another confrontation over the U.S. debt limit, which will need to be raised in the coming months. Republicans insist that any increase in the government's $16.4 trillion borrowing authority must be paired with an equal reduction in spending.
- CNBC's Steve Liesman contributed to the report.