WASHINGTON - In a test of divided government, the White House and congressional Republicans bargained in secret and sparred in public Tuesday over a deal to prevent year-end tax increases for middle class millions and spending cuts to the military as well as other federal programs.

Officials disclosed that President Barack Obama and House Speaker John Boehner had exchanged at least partial proposals in the past two days.

Details were sparse and evidence of significant progress scarcer still, although officials said the president had offered to reduce his initial demand for $1.6 trillion in higher tax revenue over a decade to $1.4 trillion. There was no indication he was relenting on his insistence - strongly opposed by most Republicans - that tax rates rise at upper incomes.

Boehner sounded unimpressed in remarks on the House floor at midday.

"The longer the White House slow-walks this process, the closer our economy gets to the fiscal cliff," he said, declaring that Obama had yet to identify specific cuts to government benefit programs that the president would support as part of an agreement that also would raise federal tax revenue.

In rebuttal, the White House swiftly detailed numerous proposals Obama has made to cut spending, including recommendations to cull $340 million from Medicare over a decade and an additional $250 billion from other government benefit programs.

The House Democratic leader, Rep. Nancy Pelosi of California, challenged Boehner to allow a vote on the president's proposal to extend most expiring tax cuts while letting them lapse at higher incomes.

She predicted it would gain "overwhelming approval," even in the GOP-controlled House.

Boehner's office took the step - unusual in secretive talks - of announcing that Republicans "sent the White House a counter-offer that would achieve tax and entitlement reform to solve our looming debt crisis and create more American jobs."

Both sides say they want a deal to prevent damage to the economy, but that stated commitment has been accompanied by a fierce battle to gain the political high ground in negotiations - and the occasional comment that one side or the other would be willing to let the deadline pass without a deal unless it got acceptable terms.

Republicans acknowledge that Obama has an advantage in one respect, citing his re-election last month after a race in which he made higher taxes on the wealthy a centerpiece of his campaign.

At the same time, Republicans hold powerful leverage of their own, the certainty that by spring the president will be forced to ask Congress to raise the government's borrowing authority. It was just such a threat that previously allowed them to extract $1 trillion in spending cuts from the White House and Democratic lawmakers, a situation that Obama has vowed he won't let happen again.

In his noontime remarks on the House floor, Boehner said, "Let's be honest. We're broke. The plan we offered is consistent with the president's call for a balanced approach."

"We're still waiting for the White House" to do the same, added the Ohio Republican.

GOP senators across the Capitol soon echoed his remarks.

"You have to ask the question, Is the president obsessed with raising taxes?" said Sen. John Thune of South Dakota, a member of the GOP leadership.

Referring to the president's occasional outside-the-Beltway trips to build public support for his position, Thune said Obama was "doing a victory lap" after the campaign.

Senate Republican leader Mitch McConnell said GOP lawmakers are determined to overhaul benefit programs so they can "meet the demographics of the country." He recently said Republicans want to curtail annual cost-of-living benefits for Social Security and other government benefits, as well as raise the age of eligibility for Medicare from 65 to 67 beginning at some point in the future.

"The president seems to think that if all he talks about are taxes, and that's all reporters write about, somehow the rest of us will magically forget that government spending is completely out of control and that he himself has been insisting on balance," McConnell said on the Senate floor.

He highlighted several government programs as examples of what he said was wasteful spending.

"A few weeks ago, Senator (Tom) Coburn issued a study that showed taxpayers are funding Moroccan pottery classes, promoting shampoo and other beauty products for cats and dogs and a video game that allows them to relive prom night," McConnell said. "Get this: Taxpayers also just spent $325,000 on a robotic squirrel named RoboSquirrel."

The two sides had presented rival initial offers in the cliff negotiations.

Obama's plan would raise $1.6 trillion in revenue over 10 years, in part by raising tax rates on incomes over $200,000 for individuals and $250,000 for couples. He has recommended $400 billion in spending cuts over a decade.

He also is seeking extension of the Social Security payroll tax cut due to expire on Jan. 1, a continuation in long-term unemployment benefits and steps to help hard-pressed homeowners and doctors who treat Medicare patients.

The White House summary noted that Obama last year signed legislation to cut more than $1 trillion from government programs over a decade, and was proposing $600 billion in additional savings from benefit programs.

It also noted that the health care law that Obama signed into law showed savings of $100 billion. Much or all of that funding came from Medicare, even though Obama's aides insisted during his successful campaign for re-election that he had not made any cuts in that program.

Boehner's plan, in addition to calling for $800 billion in new revenue, envisions $600 billion in savings over a decade from Medicare, Medicaid and other government health programs as well as $300 billion from other benefit programs and another $300 billion from other domestic programs.

It would trim annual increases in Social Security payments to beneficiaries, and it calls for gradually raising the eligibility age for Medicare from 65 to 67, beginning in a decade.

Associated Press writers Jim Kuhnhenn and Donna Cassata contributed to this story