White House Press Secretary Jay Carney countered House Democratic Leader Nancy Pelosi after she claimed it's a "false argument" to say the federal government has a spending problem.

"Of course, the president believes that we have a spending problem," Carney said Monday, adding that the problem is "specifically driven" by health care spending. "And that's just a fact."

The gentle reminder of the nation's bloated entitlement spending came after Pelosi, in an interview with "Fox News Sunday," challenged those calling for more cuts.

"We have to recognize that, which cuts really help us and which cuts hurt our future? And cuts in education, scientific research and the rest are harmful, and they are what are affected by the sequestration," she said on "Fox News Sunday." "So, it is almost a false argument to say we have a spending problem. We have a budget deficit problem that we have to address."

Though the White House countered the remark Monday, Pelosi was nevertheless aligning herself with Obama in calling for Washington to avert a looming round of budget cuts -- by replacing them with a blend of cuts and tax hikes.

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The cuts are set to kick in March 1 and will impact the Pentagon more than any other single department. Republicans want the package replaced with a less arbitrary slate of cuts. But Pelosi argued that more cuts would hurt the economy, and in turn do little to close the deficit.

Few would argue with Pelosi's claim that the government has a deficit problem. The annual deficit exceeded $1 trillion for each of the past four years, adding $6 trillion total to the national debt during President Obama's first term.

But Republicans argue that the gaping shortfall cannot be closed with tax increases alone -- and that, indeed, Washington has a rather severe spending problem.

Even many in the Democratic Party concede that the growth in entitlement spending -- on Medicare and other budget gobblers -- needs to be checked.

Some kind of agreement, even a short-term one, needs to be reached in the next few weeks to avoid $85 billion in arbitrary spending cuts next month. Pelosi stressed that Democrats want to increase revenue by closing loopholes, including those for oil companies, as opposed to raising tax rates.

Her argument is similar to the one President Obama is expected to restate Tuesday during his State of the Union address.

However, Oklahoma Rep. Tom Cole said fellow House Republicans will "absolutely not" accept tax increases as part of a deal, which would trigger the cuts to federal defense and discretionary spending.

Cole told ABC News' "This Week" that the president refused to agree to spending cuts during the recent, so-called "fiscal cliff" negotiations so Democrats are not getting revenue increases now.

"I think (sequester) is inevitable, quite frankly," he said.

Arizona Republican Sen. John McCain also said Sunday that Republicans don't want tax increases, considering they just agreed to end more than $1 trillion in income tax breaks, but suggested he might be open to closing some tax loopholes.

He also urged both parties to work together to avoid sequester, which will result in big cuts to the defense budget and roughly $1.2 trillion in total cuts over the next decade.

"I'll take responsibility as a Republican, but we've got to avoid it," said McCain, the top Republican on the Senate Armed Services Committee. "The world is a very dangerous place."