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The debt-ceiling deal moving toward a vote in Congress could easily pave the way for tax increases despite Republican claims that tax hikes are "impossible" under a deal struck with the White House to reduce spending in exchange for a debt-limit increase.

But as everyone knows, "impossible" isn't really in Washington's vocabulary.

Here's how it could happen:

After Congress enacts more than $900 billion in spending cuts to give President Obama a $900 billion lift in the nation's $14.3 trillion debt ceiling, a bipartisan committee will be formed to find roughly $1.5 trillion in additional deficit savings over the next decade.

To get there, the committee is free to look at virtually anything -- including "revenue" -- even though House Speaker John Boehner said Sunday night that current budgeting guidelines make it "impossible" for the 12-member group to approve tax hikes.

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Other officials and analysts beg to differ.

"The suggestion that it is impossible for the joint committee to raise tax revenue simply is not accurate, it's false," White House Press Secretary Jay Carney said Monday.

Tea Party-aligned Sen. Mike Lee, R-Utah, said that's one of the concerns stopping him from supporting the deal.

"Certainly, tax increases could be something that we could face," Lee told Fox News.

Boehner is able to claim no tax hikes are possible because the committee would work off the assumption that the Bush tax cuts -- all of them -- will expire in 2013. Combined with other expiring provisions, that adds up to $3.5 trillion in tax hikes over the next decade, without the committee taking any action.

"That's baked into the cake, so to speak," said Andrew Moylan, vice president of government affairs for the National Taxpayers Union.

If members are interested in raising revenue, the committee may then try to work to eliminate deductions and other special treatment in the tax code to keep revenue flowing. Boehner might not call that a tax hike -- especially if Republicans can negotiate lower rates in exchange -- but groups like the NTU do.

While many in Congress want to extend the Bush tax cuts for the middle class, the fate of the tax cuts for high earners is a matter of debate. That means leverage for Democratic negotiators.

Likewise, Obama could look to raise taxes in one of two ways -- either by having the committee eliminate special treatment in the tax code, or by letting the Bush tax cuts for high-earners expire.

"He's looking for tax increases," Moylan said. "It's going to come from one of those two sources."

The White House isn't exactly making a secret of its aspiration. A statement put out Sunday night said the committee must pair entitlement reform with "revenue-raising tax reform that asks for the most fortunate Americans to sacrifice."

If that doesn't happen, the White House said, the president could "use his veto pen to ensure nearly $1 trillion in additional deficit reduction by not extending the high-income (Bush) tax cuts."

According to the Tax Foundation, a family with two kids making $250,000 would face a tax hike of more than $3,200 if those tax cuts expire.

That option is far more objectionable to Republicans and their supporters.

As an alternative, Republicans on the new commission may be compelled to agree to a string of revenue increases through the elimination of deductions and exemptions -- things like preferences for oil and gas companies or breaks for corporate jet owners -- that Obama has talked about all along.

Carney mentioned those preferences again on Monday, when asked about what the committee could achieve. He also mentioned limiting itemized deductions for high-income earners.

How those tax changes are described is a matter of semantics. Senate Republican Leader Mitch McConnell told Fox News Radio that no matter what the committee considers, "you couldn't get a tax increase through the House of Representatives."

But he said on CBS' "Face the Nation" Sunday that "virtually every Republican I know" supports tax reform as long as it means a lower overall rate.

"The whole idea behind tax reform is to lower the rates and remove a lot of the preferences," McConnell said.

Republicans will undoubtedly press hard for entitlement changes on the committee. Moylan said that accompanying changes in the tax code that eliminate tax "preferences" might not be described by Republicans as a tax increase, provided income tax rates don't rise.

If enough lawmakers agree, the changes offered by the committee have a better chance of becoming law than the average tax hike bill would.

Under the terms of the deal, the Senate needs just a simple majority vote to approve the committee's plan and no amendments are allowed. Senate passage typically means 51 senators. Democrats have 53 senators, counting the body's two independents.

The proposal might face a tougher lift in the House -- but conservatives and liberals alike will be compelled to approve something because a slew of deep cuts to both Medicare and the military would kick in if Congress fails to act by the end of the year.

The Committee for a Responsible Federal Budget said the upcoming decisions could offer a chance for significant deficit reduction.

"It is unfortunate we couldn't do more now, but luckily we'll get two more bites at the apple -- when the committee reports at the end of this year, and when the tax cuts expire and the debt enforcement mechanism hits at the end of next year," President Maya MacGuineas said in a statement.