Washington (CNN) -- President Barack Obama ruled out any possibility of signing a short-term extension of the federal debt ceiling Monday, insisting that the time has come to tackle the nation's most pressing fiscal problems in a comprehensive way requiring bipartisan compromise on both taxes and cuts to entitlement programs.

The president continued to push for the largest deal possible -- an apparent rejection of a call by House Speaker John Boehner, R-Ohio, to focus more narrowly on spending cuts agreed to in an earlier round of negotiations.

It's time to "pull off the Band-Aid" and "eat our peas," Obama told reporters of the need for both sides to make difficult choices to address the nation's mounting federal deficits and debt. "Let's step up. Let's do it."

Noting that Republicans have pushed for decisive action on debt reduction, Obama urged them to compromise from their blanket refusal to end Bush-era tax cuts for wealthy Americans. The president said he'd be willing to push Democrats to do something they don't like -- reform Medicare and other entitlement programs that are the party's political legacy -- in an effort to reach his goal of trimming the deficit by $4 trillion over the next 10-12 years.

"Now is the time to deal with these issues," Obama declared. "If not now, when?"

There was no breakthrough during a White House meeting between Obama and congressional leaders Monday afternoon, but top Democrats and Republicans agreed to meet again Tuesday, according to a congressional aide. Senate Minority Leader Mitch McConnell, R-Kentucky, called Monday's meeting "constructive."

While dismissing a possible short-term deal covering the rest of the year, the president insisted that an agreement to increase the current $14.3 trillion debt ceiling will be reached before August 2. Treasury officials have warned that a partial default could be triggered if lawmakers fail to act by that date.

Such a failure could lead to skyrocketing interest rates and a plummeting dollar, among other things.

Obama, who promised daily meetings until a deal is reached, reiterated his warning against either party taking a "maximalist position" in the ongoing negotiations. The president insisted he is willing to take "significant heat" from his own party on issues such as entitlement reform in order to get a deal done.

Republican leaders should as well, he said, referencing GOP opposition to any increase in tax rates.

For his part, Boehner said he still has a sharp disagreement with the White House over taxes and the "extent of the entitlement problem, and what is necessary to solve it."

"It takes two to tango, and they're not there yet," Boehner said in reference to the administration.

A Republican aide with knowledge of Monday's meeting said it included one exchange in which Boehner argued that his side also would find it difficult to vote to reform entitlements, which would likely include delaying or reducing some benefits in order to cut costs.

When Obama pointed out that the Republican-controlled U.S. House had already passed a proposal that would overhaul the government-run Medicare health insurance program for senior citizens, the GOP aide said, Boehner responded: "Excuse us for trying to lead."

Two Democratic officials with knowledge of Monday's talks confirmed the exchange but noted that it wasn't tense or any kind of showdown between Obama and Boehner.

According to multiple Democratic officials familiar with the meeting, Obama again made the case for a comprehensive deal at Monday's meeting but also asked House Majority Leader Eric Cantor, R-Virginia, to explain spending cuts in a possible smaller deal that emerged from previous negotiations led by Vice President Joe Biden.

Those savings totaled about $1.8 trillion, well short of the almost $2.4 trillion that the administration seeks to raise the debt ceiling through 2012. Boehner has said any debt ceiling measure must be accompanied by spending cuts of equal value.

After Cantor's presentation, Obama made the case that bridging the difference between the spending cuts agreed to in the Biden talks and the Republican demand for a debt ceiling deal would require raising revenue, the Democratic sources said. At the same time, congressional Democrats said they need revenue increases through ending tax loopholes or other steps in order to get their caucuses to support an agreement, the sources said.

With another meeting scheduled for Tuesday, congressional participants were asked to bring ideas for closing the roughly $600 billion gap between negotiated spending cuts and further savings that Republicans say are necessary for a debt ceiling deal, the Democratic sources said.

When Obama set the Tuesday meeting for 3:45, Senate Majority Leader Harry Reid asked if that was in the morning or the afternoon and the president said, "We might get to that," according to the Democratic sources.

Earlier, Boehner repeated his insistence that the House will not pass any debt ceiling deal that includes tax increases. He also stressed that the House won't pass a deal that fails to include spending cuts larger than any debt ceiling increase while also constraining future spending.

Negotiators are trying to salvage a deal after Boehner pulled back Saturday from a proposed "grand bargain" that would have saved up to $4 trillion over the next decade. The deal reportedly fell apart over a dispute regarding eventual tax increases for the wealthiest Americans by allowing the Bush-era tax cuts to expire at the end of 2012.

While Republicans remain opposed to tax hikes, Democrats are demanding revenue increases to reduce the impact of domestic spending cuts and ensure that the richest Americans shoulder some of the burden of a deal. House and Senate progressives are also balking at the idea of reining in spending on Medicare, Medicaid and Social Security.

"We, unfortunately, remain far apart because every time we get close the Republicans move the goal posts further to the right, further and further to the far right," Rep. Steve Israel, D-New York, said Monday on CNN's "American Morning."

"We're not in this boat because America taxes too little," said Rep. Tom Price, R-Georgia. "We're in this boat because America spends too much, Washington spends too much."

The president insisted Monday that he is not looking to raise any taxes until 2013 or later. He claimed he has "bent over backward to work with the Republicans" and not force them to vote on any revenue hikes in the short term -- a politically toxic move for the GOP's conservative base.

In exchange, Obama said, he wants to ensure that the current progressive nature of the tax code is maintained, with higher-income Americans assessed higher tax rates.

An aide to Boehner said the speaker is now proposing a smaller deal based on $2.4 trillion in cuts identified during previous talks spearheaded by Vice President Joe Biden.

Boehner hinted as much at the GOP's strategy meeting on Saturday evening, when he issued a statement saying that his party cohorts could not support a major deal so long as Obama and Democrats insist on increasing taxes. He said that any such revenue-raising initiative would prevent the bulk of Republicans from supporting a more ambitious deal, even if it was one that included cutting spending and reforming entitlement programs such as Medicare.

Boehner insisted the talks' parameters should be scaled back to focus on budget cuts alone.

The White House immediately pushed back, with a senior administration official saying Boehner had initially accepted the need to increase tax rates on wealthy Americans as part of a deal. But then, the official said, Republicans offered a different plan in talks with Obama that began Thursday.

Boehner insisted Monday that he had never discussed an increase in tax rates.

At the heart of the GOP resistance is a bedrock principle pushed by conservative crusader Grover Norquist against any kind of tax increase. A pledge pushed by Norquist's group, Americans for Tax Reform, has been signed by more than 230 House members and 40 senators, almost all of them Republicans.

CNN's Ted Barrett, Kate Bolduan, Tom Cohen, Dan Lothian, Alan Silverleib, Jessica Yellin and Deirdre Walsh contributed to this report.

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