The move, which the source stressed was not Obamas 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.
Considerable work remains as both sides now try to bridge the gaps between them and then sell a package to their respective allies in the US Congress.
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, the source said on condition of anonymity. Thats up from the $250,000-threshold the president has been demanding for months, but still far from Boehners preference of $1 million.
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.
Boehners 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 programme, the source said, through the use of a different formula to calculate the regular raises called chained Consumer Price Index.
Obama and Boehner remained apart on the politically explosive issue of how and when to raise the government debt ceiling to permit the government to borrow more money.
Boehner has proposed a one-year boost in the debt ceiling, tied to spending cuts. Obama, as of Monday night, was pushing for a two-year increase, potentially a major concession that many congressional conservatives may find hard to swallow since they have used it to extract spending cuts from the White House.
Missing entirely from Obamas offer was an extension of the so-called payroll tax holiday, which comes to an end on January 1 with an immediate negative impact on wage earners.
Introduced by Obama two years ago as an economic stimulus, the tax holiday reduced an employees share of the payroll tax from 6.2% to 4.2%. Because the tax supports the Social Security program, however, there have been divisions in both parties over continuing the holiday.
Because the details were incomplete and specifics vague, particularly on such issues as cutting the Medicare, the government health insurance programme for seniors, it was uncertain how much resistance might come from Congress. But the source stressed that Mondays offer was by no means the final one from the White House.
The response from Boehners 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, emphasising 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 on Monday evening put a deal realistically within reach.
Obama and Boehner held talks at the White House earlier Monday, and aides from both parties said they were optimistic an agreement was shaping up. Rank-and-file Republicans, however, 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.
Investors were cheered earlier on Monday, before news broke of Obamas counter-offer, by signs of progress and the Standard & Poors 500 index of US stocks rose 1.19%. 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.
Boehner faces a crucial test on Tuesday morning when he is expected to brief his partys lawmakers in the Republican-controlled House. Both sides declined to say what Boehner and Obama discussed at the meeting. The White House said Boehners latest proposal does not meet its standards.