Private talks between President Obama and top congressional leaders in search of a deal to avoid the year-end “fiscal cliff” are accelerating, officials said Monday, even as the president began ramping up pressure on Republicans to extend tax cuts for the middle class.

Obama telephoned House Speaker John A. Boehner (R-Ohio) and Senate Majority Leader Harry M. Reid (D-Nev.) over the weekend, in a sign that high-level negotiations are advancing with only weeks to go before an automatic series of spending cuts and tax hikes starts to hit nearly every American.

Boehner, meanwhile, was laying plans Monday for top Republicans to meet with Erskine Bowles, a chief of staff in the Bill Clinton administration who also has close ties to Obama’s White House.

Ahead of the Wednesday meeting, GOP aides noted that Bowles offered a debt-reduction plan last fall in line with Republican principles. That plan called for $800 billion in fresh revenue through an overhaul of the tax code and significant spending cuts, including major changes to Medicare and other federal health programs.

“People in both parties agree we need a ‘balanced approach to deal’ with our deficit and debt and help our economy create jobs,” Boehner said. “We look forward to talking to Mr. Bowles and [others advocating a debt deal] about their ideas to avert the fiscal cliff without tax hikes that target small businesses and cost jobs.”

In recent days, other Republicans — such as Sens. Lindsey O. Graham (S.C.), Bob Corker (Tenn.) and Saxby Chambliss (Ga.) and Rep. Peter T. King (N.Y.) — have voiced support for a deal that includes additional tax revenue and dismissed an anti-tax pledge circulated by GOP activist Grover Norquist. Norquist has long been a potent force in GOP politics, admonishing Republicans who express any openness to increasing tax collections and organizing opposition to them.

Still, a wide gap remains between Obama and the Republicans on taxes and changes to federal retirement programs. Resolving those differences are key to avoiding the year-end tax hikes and spending cuts, which threaten to suck $500 billion out of the economy next year and snuff out the recovery.

Democrats remained Monday in a trust-but-verify posture toward Republican talk of softening opposition to increased taxes. “We need more specifics. We haven’t seen them yet,” Senate Finance Committee Chairman Max Baucus (D-Mont.) told reporters Monday, while still welcoming the rhetorical shift. “It’s not where they were before the election,” he said.

Talks began 10 days ago with a meeting between Obama and congressional leaders at the White House. That session ended with the four congressional leaders — Boehner, Reid, House Minority Leader Nancy Pelosi (D-Calif.) and Senate Minority Leader Mitch McConnell (R-Ky.) — standing side by side and expressing optimism about a potential deal. But continuing work by staff up to the Thanksgiving weekend and on Monday has not yet made enough progress for a second meeting between Obama and the congressional leaders to be scheduled.

A key dispute is how to raise taxes on the wealthy. Boehner has previously opened the door to about $800 billion in new tax revenue — achieved through an overhaul of the tax code that eliminates deductions that disproportionately benefit the rich. The speaker and other Republicans have opposed any proposal that increases tax rates.

Obama, however, favors $1.6 trillion in new tax revenue and insists that it be achieved by allowing tax rates on the wealthy to increase at the end of the year, as well as by eliminating deductions.

On Monday, White House press secretary Jay Carney made clear the president was maintaining that position. “Math tells us that you can’t get the kind of balanced approach that you need without having rates be part of the equation,” he said. “We ­haven’t seen a proposal that achieves that, a realistic proposal that achieves that.”

Carney, however, also embraced the view that any plan to tame the national debt would require adjustments to the nation’s health programs for the elderly and the poor, Medicare and Medicaid.

Obama “believes and understands that in order to achieve a deal, a compromise, that everybody has to make some tough choices, and he remains committed to that principle,” Carney said.

On the other hand, he said the White House is less interested in tackling the rising cost of Social Security during the current talks, echoing Senate Democrats who have said the program should be reviewed separately next year. “Social Security is not currently a driver of the deficit. That’s an economic fact,” he said.

In addition to pursuing private talks, the White House began making a public push on Monday. Obama is strongly considering holding events in Washington or elsewhere later this week to argue for extending current tax rates for 98 percent of Americans and letting rates rise for the wealthy, according to administration officials.

White House officials met Monday with the leaders of two major business groups — the Business Roundtable and the U.S. Chamber of Commerce — part of Obama’s campaign to persuade business executives to get behind a deal that raises $1 trillion or more in tax revenue. Obama plans another meeting with executives Wednesday.

As part of its campaign over tax rates, the White House published a report Monday warning that the average family will pay $2,200 more in taxes next year if Congress does not freeze rates for the middle class.

The White House report says Americans could dramatically pull back on spending in the crucial holiday season if they expect sharp tax hikes next year that would cut deeply into take-home pay. A tepid shopping season would interrupt a string of positive data in recent weeks that suggest Americans are opening their pocketbooks after years of post-recession caution.

If the middle-class tax cuts and related provisions were to expire, the economy could lose $200 billion in 2013, according to the White House report, which was completed by the Council of Economic Advisers and National Economic Council.

Analysts at the nonpartisan Congressional Budget Office and the independent Tax Policy Center have arrived at similar conclusions.

Consumer spending represents the lion’s share of economy activity, and nervousness about higher taxes could take a bite out of the economy as the year comes to an end. One-fifth of annual retail sales take place between now and Jan. 1.

Consumer confidence took a dive in the summer of 2011, when the nation flirted with a default on its debt and Congress was paralyzed over questions of taxes and spending.

So far, such fears are not yet apparent among consumers this holiday season. This past weekend, consumers spent $59.1 billion on holiday shopping, 13 percent more compared with last year.

The White House report says that letting the middle-class tax cuts expire — and failing to patch the alternative minimum tax, which applies to many upper-middle-class households — could trim consumer spending by 1.7 percent in 2013. That, in turn, would slow economic growth by 1.4 percent.

Paul Kane contributed to this report.