With the government shutdown one week away from snowballing into the debt ceiling, the GOP appears to be settling on a strategy to resolve both issues. Out is the quixotic drive to defund ObamaCare; in are negotiations with Democrats on a modest budget agreement.

Over the past few days, House Republicans have stumbled from one set of demands to the next, all while holding the economy hostage. In the latest round of maneuvering, House budget guru Rep. Paul Ryan (R-Wis.), writing in The Wall Street Journal, called on President Obama to negotiate on "common-sense reforms of the country's entitlement programs and tax code." Among other possibilities, that means asking well-off seniors to pay higher Medicare premiums, and opening new land to energy exploration.

One thing that was conspicuously missing: Any mention of ObamaCare.

The omission was so notable that Ryan later backtracked in the wake of a conservative backlash. "We're going to keep going after ObamaCare," he told radio host Bill Bennett. "I'm totally committed to dismantling this law."

Nevertheless, the shift — from chest-thumping about ObamaCare's supposed tyranny to polite pleas for a fiscal reality check — was a striking indication of how the GOP has quietly moved to repackage the debate.

The revised demands were "definitely less crazy than what Republicans have proposed previously," said The New Republic's Jonathan Cohn. Indeed, some commentators said Ryan's offer represented a significant breakthrough in the stalemate.

But even if we assume that Ryan is being sincere, there's still one very big problem, and it's the same problem that has dogged the GOP ever since the shutdown train began to leave the station: The Tea Party.

Speaker John Boehner (R-Ohio) has so far resisted spurning the House's right wing. But given the Ted Cruz–aligned bloc's intransigence, it's unclear whether anything short of a massive Democratic cave would placate them enough to agree to reopen the government and avoid a damaging debt default.

Even if Democrats were to accept some concessions — say, the entitlement reforms Ryan suggested in exchange for new revenue — it's hard to envision such a deal passing muster with conservative holdouts.

Here's New York's Jonathan Chait on that point:

Any bipartisan deal, even one heavily slanted to the Republican side, would enrage conservatives. Even the tiniest concession — easing sequestration, closing a couple of token tax loopholes — would be received on the right as a betrayal. Loss aversion is a strong human emotion, and especially strong among movement conservatives. Concessions given away will dwarf any winnings in their mind. Boehner, Ryan, and Cantor have spent months regaling conservatives with promises of rich ransoms to come. Coming back with an actual negotiated settlement would enrage the right. [New York Magazine]

Having promised the base a king's ransom it cannot deliver — the president's signature domestic policy achievement — the House GOP leadership has ensnared itself in a trap of its own making. Boehner can't claim merely superficial wins without risking his job, and superficial wins are all the GOP will get even in a wildly optimistic scenario.

After all, polls uniformly show the GOP getting clobbered over the shutdown. A Gallup survey out Wednesday found only 28 percent of Americans had a favorable opinion of the Republican Party, its lowest score ever in the two decades that Gallup has posed the question.

In other words, no matter what scheme Republican leaders come up with, they will still have to face the wrath of the base. For example, under one rumored plan, House Republicans would potentially back a short-term debt ceiling hike in exchange for a promise of budget negotiations later. That's right: After all this, Republicans will merely get a date with Obama at the negotiating table. Such a deal would almost surely require Democratic votes to pass, and split the Republican Party in the House.

The idea that Boehner could keep his fractious conference united while reaching an agreement with President Obama to end the stalemate has always had the quality of magical thinking. So we're back to the question that dominated the discussion before the government was shut down, and it's really the only question that matters going forward: Will Boehner split with the Tea Party or not?