Labor union leaders emerged from talks with President Barack Obama on Tuesday vowing a side-by-side battle against Republicans to bring about higher taxes on the wealthy as part of an effort to avoid the so-called fiscal cliff.

"It was a very, very positive meeting," AFL-CIO President Richard Trumka told reporters in the White House driveway after the meeting.

"The president, like we are, [is] committed to preserving the tax breaks for the middle class and making sure that rich people pay their fair share. He's very, very committed to that, we are committed to that," Trumka continued. "We are very, very committed to making sure that the middle class and workers don't end up paying the tab for a party that we didn't get to go to. And the president is committed to that as well."

The meeting, which included top Obama economic advisers like Gene Sperling and White House chief of staff Jack Lew, came a day before the president was to hold similar talks with CEOs from major companies including American Express, General Electric, Ford Motor and PepsiCo. One participant described Obama as being in "listening mode" and said the president's final negotiating position would depend in part on what he hears from the executives. The president meets Friday with top Republican and Democratic leaders.

At issue is the best way to handle the looming fiscal cliff—an economically toxic blend of tax hikes, spending cuts and end of long-term unemployment benefits. The president campaigned on a vow to extend Bush-era tax cuts that chiefly benefit families making below $250,000 a year, while letting rates rise on income above that. Republicans want to extend all the rate reductions.

Obama and his political foes are also looking for a way to avert the so-called sequester—cuts of $1.2 trillion over 10 years from domestic and military programs, triggered by Congress's failure to reach a debt-cutting deal last year. Going over the cliff could cause another recession, experts say.

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On Tuesday, White House press secretary Jay Carney said Obama was hunting for a $4 trillion deficit-cutting deal, of which $1.6 trillion would be increased tax revenue.

Liberal groups, including the AFL-CIO, have warned they will oppose attempts to curtail popular entitlement programs like Medicare or Social Security on the table.

When asked if the president would consider raising the eligibility age for Medicare, Trumka, whose union opposes such changes, said to reporters, "If I knew that, why would I talk about it here? We are pretty clear about our position on ages and benefit cuts."

National Education Association President Dennis Van Roekel told Yahoo News by telephone after the meeting that he had raised the issue of protecting Medicaid and "not decreasing the benefits of the people who have it." Van Roekel said he warned that shifting more costs to the states would have a "devastating" budgetary impact and hurt the one-third of American kids who get their health care through that program.

Asked about past confrontations when Obama drew a line in the sand only to wipe it away when Republicans wouldn't budge, Van Roekel said the election may have changed the dynamics in polarized Washington.

"His opponents have to view him differently," Van Roekel said. "Before, his opponents could leverage things. But now they've lost lots of that leverage because he's not running again."

Carney noted that "the president has made very clear that everyone, throughout this process—not just in this past week since the election, but for some time now—that the whole point of compromise is that nobody gets to achieve their maximalist position."

Still, Carney said, Obama will veto any bill that extends the Bush-era tax cuts for the richest 2 percent of Americans. "That has long been his position; it has not changed," Carney said.

Still, the NEA chief and his fellow union leaders made it clear that they're throwing their considerable political muscle behind efforts to pressure Republicans into a compromise.

"What we're going to do is keep our members mobilized and organized," said AFSCME President Lee Saunders. "We won the election, but we're going into another campaign now."

"We're united," said SEIU President Mary Kay Henry. "We need to stay as engaged as we were in the election throughout the rest of this year to make sure that we get the Republican House to say 'yes' to tax cuts for the middle class."

"Are we going to push them on that?" asked Trumka. "Without a doubt we're going to push them on that. Are we going to collectively stand up and make sure that workers get a fair share in all of this? Absolutely we are. Do we believe that the president is committed to that same thing? Absolutely we do."

On this much, at least, Obama and his labor union allies agree: The scandal that drove David Petraeus from his perch as CIA director will not distract the commander in chief from talks on the fiscal cliff.

"I didn't get the indication that very many things are going to distract the president from doing precisely what he said he would do during the campaign," Trumka said. "I hope we get through this thing with Petraeus."

Trumka pointed to the May 2011 raid in which elite American forces killed Osama bin Laden. "No one knew what was going on. He was able to handle that, and I think this is very less distracting than that ever could have been," he said. "So I don't have any concerns at all about it. I know the president's capability, and I know that he'll handle this thing, and nothing will take away his focus."