WASHINGTON, Dec. 11, 2012 -- As the clock ticks toward a tax hike on all Americans in 20 days, President Obama predicted Republicans would join Democrats to extend current rates for 98 percent of earners before the end of the year.

"I'm pretty confident that Republicans would not hold middle class taxes hostage to trying to protect tax cuts for high-income individuals," Obama said today in an exclusive interview with ABC News' Barbara Walters.

"I don't think they'll do that," he said of Republicans forcing tax-rate increases for families earning $250,000 a year or less.

The sign of optimism follows weeks of tense negotiations and public posturing to avert the so-called "fiscal cliff," an economically toxic package of $6 trillion in across-the-board tax hikes and $1.2 trillion in deep spending cuts that could begin in early 2013.

The White House and House Speaker John Boehner have exchanged new, competing deficit-reduction plans over the last 24 hours, sources say, but there is little indication of real progress toward a deal.

Obama has taken a hard line against extending current, lower tax rates on income over $250,000, which would affect the top 2 percent of income-earners. Republicans have said those rates should be extended.

The standoff threatens higher rates for everyone unless a broad "cliff" deal is reached, or the middle-income rates are extended on their own.

"I remain optimistic," Obama told Walters. "I'd like to see a big package. But the most important thing we can do is make sure that middle class taxes do not go up on Jan. 1."

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Obama met privately with Boehner at the White House on Sunday for their second face-to-face session on the fiscal negotiations, signaling potential progress toward an agreement. But neither side presented specific details about the outcome of the meeting.

"I think the tone was good," Obama told Walters. "I believe that both Speaker Boehner and myself and the other leaders want to see a deal happen. And the question now is can we get it done. The outlines, the framework of what a deal should look like are pretty straightforward."

While the administration has emphasized tax increases on the wealthy, Republicans insist they need specific commitments from the White House on cuts to entitlement program spending, which are the primary drivers of federal deficits and debt.

"It was a nice meeting, it was cordial," Boehner said today of his Sunday meeting. "But we're still waiting for the White House to identify what spending cuts the president is willing to make as part of the 'balanced approach' that he promised the American people."

Boehner and House Republicans have proposed curbing the rate of increase for Social Security payments and raising the eligibility age for Medicare, among other changes, which are non-starters for many Obama supporters.

In his interview with Walters, the president hinted at new flexibility on entitlement spending cuts, but only once Republicans concede on top tax rates.

"If the Republicans can move on that [taxes] then we are prepared to do some tough things on the spending side," Obama said. "Taxes are going to go up one way or another. And I think the key is that taxes go up on high-end individuals."

Raising the Medicare eligibility age from 65 to 67 is "something that's been floated," Obama said, not dismissing the idea outright.

"When you look at the evidence, it's not clear that it actually saves a lot of money," he said. "But what I've said is let's look at every avenue, because what is true is we need to strengthen Social Security, we need to strengthen Medicare for future generations, the current path is not sustainable because we've got an aging population and health care costs are shooting up so quickly."

ABC News' Jonathan Karl contributed to this report.