Whether or not that’s true remains an open question. It’s already the subject of renewed partisan sniping even amidst a bipartisan breakthrough, and the likely focus of a debate that will consume Washington into the fall and beyond.

The GOP’s commitment to opposing tax hikes of any size or stripe, hardened in the course of the debt-ceiling fight, is now party orthodoxy. And the right scored a major tactical win in forcing President Obama to abandon demands that new revenues accompany upfront spending cuts prescribed by the package the House approved Monday.

But the agreement the parties reached is complex, setting up a months-long push by a special committee of lawmakers to continue work on deficit reduction measures. Even as the parties were rolling out details on Sunday night to their respective rank-and-file, they began a fresh round of back-and-forth about whether and how deeply the committee can dip into the tax code for new revenue.

The dispute turns on two questions, one technical and the other practical. Technically, the committee will have relative free range to rework the tax code. Practically, it may have its hands tied.

First, the technical case. A PowerPoint presentation Speaker John Boehner’s (R-Ohio) office used to sell the deal to House Republicans argued the committee’s framework effectively made it impossible for the panel to raise taxes. The reason, the Speaker’s office maintained, is that the panel will be working off of a budget baseline pegged to current law. And under current law, the Bush tax cuts for all income levels are set to expire at the end of 2012.

Ordinarily, Republicans would defer to current policy, not current law. That is, with the Bush tax cuts on the books, they contend that not extending the breaks amounts to a tax hike. The GOP used that argument at the end of last year to beat back attempts by the White House to extend only the cuts for low- and middle-income earners. The Democrats’ plan wasn’t a tax cut for lower income earners, Republicans said, but a tax hike on the higher end.

In this case, because the official budget scorekeepers at the Congressional Budget Office are counting on all of the cuts to expire, they would score an attempt to extend them as a deficit-busting tax cut. So for the purposes of the committee, the Republicans are reversing course and embracing the tax-extension-as-tax-cut model: if Democrats try to extend the cuts for, say, people earning under $250,000 a year, the CBO will count the move as a counterproductive cost weighing against the panel’s deficit reduction efforts.

Even split: Compromise or deadlock?

There are two issues with the Speaker’s technical case. For one, as White House spokesman Jay Carney and other Democrats noted on Monday, if the committee wants to work off of another budget baseline — one that doesn’t count on the Bush tax cuts expiring, for example — its members can simply agree to do that.

More significantly, regardless of the baseline, the majority of the Bush tax cuts are focused on the individual side of the tax code. The corporate loopholes that President Obama has wielded for months to argue that Republicans are more interested in protecting corporate jet owners and Big Oil companies rather than the middle class? All fair game for the committee.

But for either of these considerations to actually be in play will require majority support on the committee, which brings us to the practical case. The committee’s membership will be split evenly, with each party naming three of its own from the House and three more from the Senate. The twelve lawmakers have until Thanksgiving to deliver a plan for at least $1.2 trillion in deficit reduction over the next decade.

If they fail to reach agreement, those savings would be enacted automatically by painful cuts split between Republican and Democratic priorities: the Pentagon and domestic programs. All Republicans need to do to ensure tax hikes don’t enter the mix is apply a litmus test to their appointees, naming only committed anti-revenue lawmakers.

But the dynamic sets up a prisoner’s dilemma. If Republicans name hardliners to the panel, they are likely to end up having to swallow the deep defense cuts triggered by the fallback option. If Democrats name hardliners too, it would create a deadlock on the committee that activates the trigger. If Democrats name moderates who cut a deal, it would then likely fail in the Democratic-controlled Senate.

For the committee to forge a package that has a chance of passage in both chambers, Republicans will need to tap lawmakers ready to talk taxes. In that, the profile of the GOP appointees will reflect the party’s commitment to its new anti-tax orthodoxy.