If President Obama knew then what he knows now, he would not have voted against raising the debt limit in 2006.

That was the explanation trotted out by the White House Monday, as it sought to square the administration's pleas to Congress to lift the debt ceiling by next month against Obama's voting history. As a senator in 2006, Obama voted against raising the debt limit. But White House Press Secretary Jay Carney said the president now views that vote as a "mistake."

"He now believes it was a mistake," Carney said. He said Obama understands that senators want to make it clear when they disagree with the administration but that there are other ways to go about doing it. He said the debt ceiling vote is not something Washington "can play around with," warning that a failure to lift the cap would be "Armageddon-like" for the economy.

The White House tried to clear up questions about the debt ceiling ahead of a critical speech Wednesday in which he'll outline a new deficit-reduction plan -- a proposal no doubt meant to convince Republicans that he's serious about spending cuts and that there's no need to hold the debt ceiling vote "hostage."

"He will very clearly lay out his vision for deficit reduction, the need for it to be balanced, the need for it to be bipartisan, the need for it to address the long-term drivers of our debt and for everyone to share in the burden of bringing our fiscal house into order," Carney said.

"We believe that we should move quickly to raise the debt limit and we support a clean piece of legislation to do that," he added. "Concurrently -- not linked, but concurrently -- the president is going to demonstrate on Wednesday his commitment again to deficit reduction."

Treasury Secretary Tim Geithner now estimates that the nation's debt ceiling will be reached no later than May 16, and has urged Congress to act before then. In a letter to Senate Majority Leader Harry Reid, Geithner wrote that Congress risks a fiscal calamity potentially worse than the one from which the nation is recovering.

Geithner noted that the Treasury Department can take "extraordinary measures" to buy time -- about eight extra weeks, maximum -- after the May deadline. But he said once those measures are exhausted the U.S. government would not have enough money to pay its bills. Military salaries, Social Security payments and jobless benefits would cease, he warned, adding that a default on the debt would drive up interest rates, erode home values and cause a new financial crisis.

"For these reasons, default by the United States is unthinkable," Geithner wrote.

But after extracting a last-minute budget deal out of Democrats, in turn averting a government shutdown and marking billions of dollars in spending cuts in their column, Republicans are in the mood for another stand-off on Capitol Hill. From the top down, GOP leaders warn they will not vote to raise the $14.3 trillion debt ceiling unless they see genuine efforts to reduce the deficit.

"There will not be an increase in the debt limit without something really, really big attached to it," House Speaker John Boehner said at a fundraiser Saturday night.

In an interview with Fox News on Monday, Boehner reiterated that his members will not vote to raise the cap without "serious steps" on spending cuts. He acknowledged that leaving the cap in place would have "very serious implications for the worldwide economy and jobs here in America," but said Republicans will not "roll over" without addressing the underlying problem.

"The biggest threat that we have to our economy and to our future is doing nothing, and that's what the president asked us to do -- do nothing," Boehner told Fox News. "Doing nothing is totally irresponsible and we will not go down that path."

Boehner said there will be "dozens" of spending battles over the next year and a half.

Republicans are touting Rep. Paul Ryan's, R-Wis., budget proposal -- a plan released last week that contains about $6 trillion in spending cuts over the next 10 years -- and suggest they'll be pushing for some of its provisions. Ryan, in an interview with NBC's "Meet the Press," said the Republicans' strategy is not to default, but compel the government to control spending.

"I think there will be some kind of negotiations, and yes, it probably will go up to some sort of a deadline. The debt ceiling deadline is a moving deadline; it's not a date-certain deadline like the government shutdown," Ryan said. He said the debt ceiling increase, if Republicans are to support it, must come with "real fiscal reforms, real spending cuts, and real spending controls going forward so we can deal with the debt in the future."

White House senior adviser David Plouffe, over the course of several television interviews Sunday, indicated that the White House is willing to put some reforms on the table. Obama plans to detail some of them in the speech on deficit reduction Wednesday -- a follow-up to a budget proposal earlier in the year which was widely panned by Republicans as doing little to control spending. Amid the back-and-forth, Obama took a moment Monday afternoon to speak with a group of Colorado students touring the White House. He told the tour group that education will stay a priority for him in budget talks going forward.

But the White House warns that voting against the debt ceiling increase would be "catastrophic" for the economy.

Carney on Monday urged Republicans not to hold the debt limit vote "hostage" in order to extract budgetary concessions. He said the president is serious about cutting spending, but that Congress should not "play chicken" with the economy.

Sen. Charles Schumer, D-N.Y., urged Republicans to take the debt-limit threat off the table.

"It could be a formula for recession or worse," Schumer told CBS' "Face the Nation." "So this is playing with fire."

Though Geithner, in his letter to Reid, said Treasury has a few tricks up its sleeve to forestall the default deadline, he noted the government has "much less flexibility" than it used to because of the sheer size of its deficits.

The secretary said the U.S. government, for instance, can't simply cut spending or raise taxes to avoid hitting the cap. With the public debt increasing at a rate of about $125 billion every month, Geithner said it would take an impossible amount of budgetary rearranging to halt that climb in the near-term.

For reference, the projected fiscal 2011 deficit was about $1.6 trillion. After weeks of wrangling, Congress cut that by just $38.5 billion in the deal reached over the weekend.

"In order to avoid an increase in the debt limit, Congress would need to eliminate annual deficits immediately," Geithner wrote.