Speaking a few hours after Obama and Boehner met at the White House, these people said the president was now seeking a higher tax rate beginning at incomes over $400,000, up from the levels of $200,000 for individuals and $250,000 for couples that were cornerstones of his successful campaign for re-election.

Obama’s willingness to reduce future cost-of-living increases in Social Security, government retirement and numerous other programs marked another clear a concession to Boehner, although it came with an asterisk. The president wants lower-income recipients to receive protection against any loss from scaling back future cost of living increases, these officials said.

Nor did Obama’s offer include raising the age of Medicare eligibility from 65 to 67, a Republican goal that has drawn particularly strong objections from Democratic liberals.

Several officials also said during the day that Boehner’s offer late last week to accept higher tax rates included provisions that would mean higher taxes on investment income and dividends earned by wealthy Americans and also in the estate tax.

The people who described the talks did so on condition of anonymity, citing the secretive nature of the discussions.

The maneuvering is aimed at reaching an agreement that would include cancellation of a scheduled year-end hike in taxes for nearly all wage-earners as well as spending cuts at the Pentagon and in domestic programs across the government.

Economists inside and outside the government have warned that the combination of the two, set to begin at year’s end, could send the economy into recession.

Other major issues are part of the negotiations. Without action by Congress, for example, long-term unemployment benefits will expire for millions at the end of the year, and doctors will face a cut in the payments they receive for treating Medicare patients.

Obama has also called for assistance for hard-pressed homeowners as well as fresh economic stimulus measures, and some Democrats want to include a sizeable amount of disaster aid in any legislation to offset the cost of Superstorm Sandy.

On other points, Obama’s latest offer dropped his earlier proposal to extend a payroll tax cut due to expire at year’s end, and he agreed to find more savings in government spending than in his earlier offer.

The new offer that was given to Boehner at the White House closed the gap between the two men considerably on a framework for a deal.

At the same time, with rank and file conservatives distressed about over higher taxes, aides to the Ohio Republican were quick to find fault with Obama’s latest offer.

Brendan Buck, a spokesman, said that “a proposal that includes $1.3 trillion in revenue for only $930 billion in spending cuts cannot be considered balanced. We hope to continue discussions with the president so we can reach an agreement that is truly balanced and begins to solve out spending problems.”

Earlier, at the White House, spokesman Jay Carney sidestepped when asked about curbing cost-of-living increases for benefit programs. The president “is prepared to make tough choices. He also understands that his bill will not, as written, likely be what the final compromise, if there is one, looks like,” he said.

“But he insists and will insist before he signed anything that there is the balance that he seeks that is fair and that seniors aren’t bearing the burden so that the healthy bear less — those who can afford it most bear less.”

A spokesman for Boehner declined comment on the tax proposals.

Obama and Treasury Secretary Tim Geithner met with Boehner and his top aides at the White House for less than an hour during the day. While neither side provided significant details, Republicans have made it clear in recent days that it is the president’s turn to propose savings from Medicare and other benefit program following Boehner’s agreement last week to let tax rates rise at incomes higher than $1 million.

Officials familiar with the talks said that under the Ohio Republican’s proposal, the top tax rate on capital gains would go to 20 percent, up from the current 15 percent. The top rate on dividends also would climb, although it was not known what the new level would be, and the estate tax would also be adjusted to produce more government revenue.

Under current law, the top capital gains tax rate would rise to 20 percent automatically at the end of the year if the cuts enacted during George W. Bush’s White House tenure were allowed to expire.

The tax on dividends would also rise. The estate tax would be 55 percent on estates after allowance for a $1 million exemption.

As the talks progress, Republicans across the party’s spectrum are eager to turn public attention toward spending cuts, rather than remain bogged down in a politically debilitating debate about tax increases.

“Our problem isn’t that we tax too little. It’s that we spend too much! We must have serious spending cuts for a debt ceiling increase,” tweeted Rep. Tom Price., R-Ga.

That was a reference to the third ingredient under negotiation as part of deal to prevent the economy from reaching the fiscal cliff — an increase in the government’s borrowing authority.

After a brush with the first-ever default by the Treasury in 2011, Obama is demanding that any fiscal cliff compromise give him authority to raise the current $16.4 trillion cap without a prior vote by Congress. Officials say that Boehner’s most recent proposal would grant an increase equal to the size of any spending cuts, roughly $1 trillion under his own recommendations.

The speaker made his offer to Obama late last week, dropping his blanket opposition to the president’s call for an increase in the tax rate paid on upper incomes. Obama’s agreement to reduce his demand so it would affect incomes over $400,000 left the two sides closer, but short of agreement.

As part of the change, Obama is now seeking $1.2 trillion in additional revenue, down from $1.4 trillion that was in an offer he made several days ago.

Officials have said Boehner offered a total of $1 trillion in higher revenue, less than half of which would come this year, and the balance in 2013 as part of a bill to overhaul the tax code.

Some of the increased revenue to be provided immediately would come from setting the tax rate on income over $1 million at 39.5 percent, up from the current 35 percent. The balance would come from higher taxes on capital gains, dividends and other provisions.

The proposal to scale back cost-of-living increases is a regular at deficit reduction talks.

Obama tentatively agreed to back it more than a year ago in talks with Boehner that eventually collapsed, although he sought steps to shelter the lowest-income beneficiaries from its effects.

Democrats have said they would object much more strongly if the president would to accept a plan to raise the Medicare eligibility age from 65 to 67. He was ready to embrace that proposal in the earlier round of talks, but he would face opposition from congressional Democrats and the AARP as well as other groups in the current political climate.

The new inflation adjustment would create government savings of an estimated $168 billion over a decade, according to a recent estimate by the Congressional Budget Office. It also would raise tax revenue by $54 billion by affecting the adjustment in income tax brackets that occurs annually to take inflation into account, CBO said.