WASHINGTON -- President Barack Obama and House Speaker John Boehner inched closer to a solution to avert a looming fiscal crisis Tuesday with a deal that would fail to meet one of the president’s top campaign pledges of raising taxes on the wealthiest 2 percent of Americans.

The White House and Republicans in the House of Representatives traded barbs publicly throughout the day, but privately the two sides weren’t that far apart on a compromise that could avoid a series of drastic spending cuts and tax increases that would threaten to push the nation back into a recession.

The proposed solution includes raising taxes for households with annual incomes of more than $400,000, up from the $250,000 income level Obama had campaigned on for months at rally after rally as he sought re-election this year. That comes to less than 1 percent of the nation’s top earners.

Administration officials defended the proposed package Tuesday, saying the president is willing to do what it takes to avoid the end-of-the-year deadline of the so-called fiscal cliff.

“The fact that he’s willing to compromise . . . demonstrates his good-faith effort here to reach a compromise and still have a package that is balanced and asks the wealthiest to pay more, enacts significant spending cuts and puts us on a fiscally sustainable path,” White House spokesman Jay Carney said.

Obama on Monday offered a plan that reduces the amount of new taxes he’s demanding to $1.2 trillion over the next 10 years, down from $1.4 trillion, and applies a less-generous measure of inflation to Social Security and other programs. But Republicans are skeptical of the White House’s calculations on budget cuts, raising questions about the savings on interest.

Asked whether a deal could be reached in the next 24 to 48 hours, Boehner said, “I’ve made it clear to the president that I would put a trillion dollars’ worth of revenue on the table if he were willing to put a trillion dollars of spending reductions on the table. That, at this point, would be my version of a balanced approach.”

The bigger controversy is likely to involve whether Obama and Boehner, an Ohio Republican, can sell a plan to the lawmakers who have to approve it.

Many Republicans remain resistant to raising any taxes. Boehner told a closed-door meeting of House of Representatives Republicans on Tuesday that he’ll seek a vote later this week on a “Plan B” that would raise taxes on million-dollar earners. Everyone else would continue to pay the current tax rates, which are due to expire at the end of the year. The plan got a mixed reaction from Republicans.

But a vote on a millionaires’ tax could help push a deal along, because it would show Boehner how many Republicans are at least willing to back some tax increases.

Democrats have been sympathetic to such proposals in the past, but they quickly distanced themselves from the maneuver this time.

“Speaker Boehner’s ‘Plan B’ is the farthest thing from a balanced approach. It will not protect middle-class families because it cannot pass both houses of Congress,” said Senate Majority Leader Harry Reid, D-Nev. Democrats control 52 of the Senate’s 100 seats.

Democrats faced some turmoil of their own, as interest groups, as well as many in their party, weren’t pleased with the White House proposal to change how the Social Security cost of living is calculated.