Democrats and Republicans are already disagreeing about what they agreed to in the recently signed-into-law deal to raise the debt ceiling, and not surprisingly, taxes are at the heart of the dispute.

Though the members of a new Joint Committee on Deficit Reduction haven’t yet been named, House Republicans and the White House have battled over budget assumptions in a wonk-vs.-wonk showdown over whether the committee would be able to raise taxes.

Of course, the issue of taxes and whether to raise them to cover the current budget shortfalls has proved to be one of the insurmountable issues between the parties during the debt and deficit debate. It’s the reason Speaker John Boehner (R-Ohio) twice walked away from talks with President Barack Obama, the reason House Majority Leader Eric Cantor (R-Va.) bowed out of bipartisan negotiations led by Vice President Joseph Biden, and ultimately, it’s the reason tax revenues were not addressed in the debt limit deal signed last week by Obama.

Senate Majority Leader Harry Reid warned last week that the conflict could derail the committee’s work. “If there’s continual talk by Republicans in the House and the Senate that there will be no revenue, then there will be no bill,” the Nevada Democrat said in an interview with NPR.

The wonky part of the dispute centers on which ruler — known as the baseline in budget parlance — will be used to use to measure the savings identified by the new 12-person committee, which was created by the law and charged with finding by Nov. 23 at least $1.2 trillion in deficit reduction over 10 years.

The argument made by House Republicans — and expounded on by House Budget Chairman Paul Ryan (R-Wis.) in an Aug. 2 blog post — is that the new law instructs the committee to use the Congressional Budget Office’s current law baseline, which assumes the 2001 and 2003 tax cuts implemented under President George W. Bush expire as scheduled at the end of 2012.

Extending those tax cuts just for the middle class but not the wealthy — as Obama has proposed — would still count as a giant tax cut, making it close to impossible to achieve the $1.2 trillion minimum deficit reduction target for the new joint committee.

The House GOP also contends that “the committee product must pass Congress, which means it must be scored by [the] CBO, using their baseline,” a House GOP aide said.

Boehner offered that line of reasoning to sell the deal to House Republicans. He used a PowerPoint presentation that declared tax increases would be “essentially impossible.”

But the White House and Congressional Democrats take issue with Boehner’s argument.

Obama administration economic adviser Gene Sperling argued in an Aug. 1 blog post of his own that it’s up to the committee to choose its own baseline, notwithstanding a reference in the new law citing the existing CBO baseline.

The new law “does not anywhere require the joint committee to work off a current law baseline,” Sperling wrote, noting that Congress frequently instructs the CBO to use alternative baselines, including for Ryan’s own budget.

And even if the panel does use the CBO assumptions, there are plenty of other tax increases that would score as deficit reduction, Sperling noted, such as eliminating tax subsidies for oil companies or corporate jets.

“These types of tax changes have been a major part of the recent deficit reduction conversation and would be a smart part of an overall balanced plan,” Sperling wrote.

Indeed, the potential tax increases that would count as deficit reduction by the CBO are nearly infinite — including shrinking business and individual deductions and an Obama proposal to create parity between wealthy and middle-class tax deductions.

But many lawmakers, including Senate Minority Leader Mitch McConnell (R-Ky.), would prefer the committee consider a broader package that includes tax code reform.

One example is the bipartisan “gang of six” Senate plan, which has not yet been scored by the CBO. But it is unclear whether it would qualify under the House Republicans’ interpretation of the baseline issue.

Maya MacGuineas, president of the Committee for a Responsible Federal Budget, said the gang of six plan is important because it eliminates the alternative minimum tax. The AMT is not indexed for inflation and is typically patched each year by Congress to avoid hitting more taxpayers.

“One of the big concerns we have is that a lot of the budget time bombs that are out there will be ignored, so any reform plan that doesn’t fix the AMT [for example] just means they are trying to fix the problem by papering over some of the outstanding issues,” MacGuineas said.

However, one item that would qualify is the $1.3 trillion war spending cut proposed by Reid in his deficit reduction bill.

Republicans dismiss the war spending cuts as “gimmicks” because the White House already plans to wind down war spending. But the CBO scores them as cuts.

“We should never underestimate the ability of policymakers to find bipartisan ways around tough choices,” MacGuineas warned. “But if they even attempt to go after those war savings, people should scream bloody gimmicking.”

But there is a further issue that seems more likely to be the major hurdle for the deal to clear: Can an agreement with tax increases even pass the House?

Republicans have already signaled that they would not support a deficit reduction package that uses tax increases, and Democrats will not likely support a package of just spending cuts.

Even if Democrats get one of the six Republicans on the panel to back a deal with tax increases, it’s unlikely the package would win enough votes to get through the Republican-run House.

That calculus, of course, could change, with a $1.2 trillion spending cut trigger taking effect starting in 2013. Half would come from security spending favored by the GOP. Reid warned last week that Democrats would pull that trigger unless Republicans agree to some revenue increases on the committee.