Republicans should “peel off the war paint” and take the deal he’s offering, Obama said sharply at the White House. He buttressed his case by noting he had won re-election with a call for higher taxes on the wealthy, then added pointedly that the nation aches for conciliation, not a contest of ideologies, after last week’s mass murder at a Connecticut elementary school.

But he drew a quick retort from Boehner when the White House threatened to veto a fallback bill drafted by House Republicans that would prevent tax increases for all but million-dollar earners. The president will bear responsibility for “the largest tax increase in history” if he makes good on that threat, the Ohio Republican declared.

In fact, it’s unlikely the legislation will get that far as divided government careens into the final few days of a struggle that affects the pocketbooks of millions and blends lasting policy differences with deep political mistrust.

Boehner expressed confidence the Republicans’ narrow so-called Plan B bill would clear the House on Thursday despite opposition from some conservative, anti-tax dissidents, but a cold reception awaits in the Democratic-controlled Senate.

As for a broader agreement, officials said there had been little if any progress toward closing the gap between the two sides in the past two days, even though aides to the president and Boehner have remained in contact.

On paper, the two sides are relatively close to an agreement on major issues, each having offered concessions in an intensive round of talks that began late last week.

But political considerations are substantial, particularly for Republicans.

After two decades of resolutely opposing any tax increases, Boehner is seeking votes from fellow Republicans for legislation that tacitly lets rates rise on million-dollar income tax filers. The measure would raise revenue by slightly more than $300 billion over a decade than if all of the Bush-era tax cuts remained in effect.

But Boehner’s office trumpeted another figure — an estimate that claimed it would amount to a tax cut of nearly $4 trillion compared with what would happen if all those tax cuts were to expire as scheduled with the turn of the year.

Similarly, despite vehement protests that the looming across-the-board spending cuts would seriously affect the Pentagon, the leadership’s fallback bill does nothing to blunt or eliminate the reductions scheduled to begin on Jan. 1

Boehner won a letter of cramped support from anti-tax activist Grover Norquist during the day. Norquist’s organization, Americans For Tax Reform, issued a statement saying it will not consider a vote for the bill a violation of a no-tax-increase pledge that many Republicans have signed.

But another conservative group came to an opposing conclusion. “Allowing a tax increase to hit a certain segment of Americans and small businesses is not a solution; it is a political ploy,” said the Heritage Foundation said in a statement.

As for the scheduled defense cuts, Rep. C.W. (Bill) Young of Florida, who heads the House panel with jurisdiction over the Pentagon’s budget, said he is undecided how to vote on the legislation.

“This is not a game. This is real because so much of the sequester (spending cuts) would be defense — half of it,” he said. “I just don’t think it’s workable.”

Rep. Tom Rooney of Florida, a member of the Armed Services Committee, said he will vote for the legislation even if it leaves the defense cuts in place. He said if he didn’t vote for a bill that prevents a tax increase for 99 percent of people “I’m not doing my job.”

That appeared to be the hope of Boehner and the rest of the leadership, that by showing his rank and file is united behind the fallback bill, the speaker would be in a strong position to demand concessions from the White House in the broader endgame.

Democrats had their own issues, but so far, they have remained largely submerged as Republicans struggle.

Reps. Peter DeFazio of Oregon and Jim McDermott of Washington, both veteran liberals, announced their opposition to a provision that Obama is backing to slow the growth of cost-of-living benefits for Social Security and other benefit programs.

At the White House, Obama repeated that he is ready to agree to spending cuts that may cause distress among some fellow Democrats, but he saved his sharpest words for Republicans.

“Goodness, if this past week has done anything, it should just give us some perspective,” he said in a reference to the shootings of school children in Connecticut.

Yet even as he implored Republicans to “take the deal,” he made it clear he’s open to more bargaining.

Asked whether he might be flexible on the level at which tax rates should rise, he said he wasn’t going to bargain in public. He also addressed the issue of politics.

Speaking of Republicans, he said, “It is very hard for them to say yes to me. But at some point, they’ve got to take me out of it.”

He added, “I’m often reminded when I speak to the Republican leadership that the majority of their caucus’ membership come from districts that I lost. And so sometimes they may not see an incentive in cooperating with me, in part because they’re more concerned about challenges from a tea party candidate, or challenges from the right, and cooperating with me may make them vulnerable.”

Nor did Boehner slam the door on further compromises in his brief appearance before reporters. “Republicans continue to work toward avoiding the fiscal cliff,” he said.

In the talks to date, Obama is now seeking $1.2 trillion in higher tax revenue, down from the $1.6 trillion he initially sought. He also has softened his demand for higher tax rates on household incomes so they would apply to incomes over $400,000 instead of the $250,000 he cited during his successful campaign for a new term.

He also has offered more than $800 billion in spending cuts over a decade, half of it from Medicare and Medicaid, $200 million farm and other benefit programs, $100 billion from defense and $100 billion from a broad swath of government accounts ranging from parks to transportation and education.

In a key concession to Republicans, the president also has agreed to slow the rise in cost-of-living-increases in Social Security and other benefit programs, at a savings estimated at about $130 billion over a decade.

By contrast, Boehner’s most recent offer allowed for $1 trillion in higher taxes over a decade, with higher rates for annual incomes over $1 million. He’s also seeking about $1 trillion in spending cuts.

The two sides disagree, too, over increases in the government’s debt limit, which will soon need to be raised when borrowing reaches the current $16.4 trillion cap.

Also at issue are unemployment benefits, which are scheduled to expire for an estimated 2 million out-of-work Americans at year’s end, and the prospect of reduced payments beginning Jan. 1 for doctors who care for Medicare patients.