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President Obama's has offered to raise the Medicare eligibility age from 65 to 67 as part of a larger deficit-reduction package, a move sure to anger congressional Democrats who want to exclude entitlement programs from the ongoing talks.

Democrats already have criticized Republicans over proposed cuts to programs such as Social Security and Medicare, and with Obama showing he is open to program changes, some Democrats are taking a hard line.

"As long as the entitlement programs are part of a cut program, I can't support it," Rep. Raul Grijalva, D-Ariz., told Fox News, calling such cuts a political and fiscal "mistake."

"Medicare, Medicaid, Social Security -- we should deal with them ... separate and beyond the discussions that tie their existence to this debt ceiling discussion."

As bipartisan talks continued Monday, two sources outside the White House confirmed to Fox News that Obama, during an earlier meeting with lawmakers Sunday night, offered to raise the Medicare eligibility age. There was also discussion of moving to a system that ties the Medicare qualification age to actuarial tables rather than a determination by Congress.

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However, lawmakers could not agree on the subject since it would have been part of a deal that included tax increases -- something Republicans vehemently oppose.

With lawmakers on Monday holding their third round of bipartisan talks since last week, Obama urged both sides to give ground. He called out Democrats for resisting entitlement cuts and Republicans for resisting tax increases.

"If each side wants 100 percent of what its ideological predispositions are, then we can't get anything done," he said.

He particularly criticized rank-and-file Republicans for allegedly hamstringing House Speaker John Boehner, claiming those members have complicated the talks by taking "irresponsible" positions.

"I think he'd like to do something," Obama said of Boehner, calling him "very sincere." "But his politics in his caucus are very difficult. That's the problem with a political process where folks are rewarded for saying irresponsible things."

He said a "my way or the highway" approach will not produce a deal. "I don't see a path to a deal if they don't budge. Period," Obama said.

The president spoke at a press conference Monday before entering the meeting in the afternoon.

But Boehner, minutes before the meeting began, said the reality is that a deficit-reduction package that raises taxes simply cannot pass the House.

"Adding tax increases to the equation doesn't balance anything," Boehner said. "The American people understand that tax hikes destroy jobs."

Boehner, describing the policy divide between the two parties as a "gulf," suggested that Democrats still weren't putting enough on the table in terms of entitlement reform.

After a head-spinning few days, Obama made clear he still wants a "serious" deal to prove to Americans that "this town can actually do something once in a while."

"Now is the time to deal with these issues," Obama said. "If not now, when?" He also urged lawmakers not to settle for a "stopgap solution" on the debt ceiling.

"We don't manage our affairs in three-month increments," Obama said. "We're going to resolve this, and we're going to resolve this for a reasonable period of time. And we're going to resolve it in a serious way."

The unsteady talks have taken several turns in recent days. After the White House built up hopes after Thursday's meeting about the possibility of a "grand bargain" dealing with everything from discretionary spending to entitlements to tax reform, Boehner on Saturday urged all sides to lower their sights and focus on a deficit-reduction package worth far less.

Republicans claimed Democrats would not back off their call for tax hikes and would not get serious about entitlements. Democrats, though, said they were in favor of a big deal all along and claimed Republicans were backing out only because they didn't want tax hikes.

The upcoming meeting, which follows a sit-down Sunday evening, is expected to focus on the terms for a deal outlined in now-defunct talks led by Vice President Biden. Those talks centered on a potential package that would achieve at least $2 trillion in deficit-reduction over the next decade -- in exchange for a vote in Congress to raise the $14.3 trillion debt ceiling.

The Obama administration claims lawmakers must raise the cap by Aug. 2 or risk the U.S. defaulting on its obligations.