With the government shutdown now dragging into Day Four, there’s increasing chatter this morning that Republicans are trying to steer the debate away from Obamacare and are trying to roll the government shutdown battle into a fight over the debt limit. The idea seems to be that this will somehow increase Republicans’ leverage.

But the very vagueness of the strategy is now becoming a serious problem among top Republicans, who are furious with conservatives for leaving the party in this position. And conservatives have no answer for them; they can’t articulate a way out of it, either. The New York Times reports on an anecdote that perfectly captures where we are:

On Wednesday at a private luncheon, several Senate Republicans — Dan Coats of Indiana, Ron Johnson of Wisconsin and Kelly Ayotte of New Hampshire — assailed Senator Ted Cruz of Texas, who has led the movement to block funding for the health law.

Ms. Ayotte was especially furious, according to two people present, and waved a printout from a conservative group friendly to Mr. Cruz attacking 25 of his fellow Republican senators for supporting a procedural vote that the group counted as support of the health law.

Ms. Ayotte asked Mr. Cruz to disavow the group’s effort and demanded he explain his strategy. When he did not, several other senators — including Mr. Johnson, Mr. Coats and even Mitch McConnell, the minority leader — joined in the criticism of Mr. Cruz “It just started a lynch mob,” said a senator who was present.

Despite the uproar, Mr. Cruz did not offer a plan for how his party could prevail in the shutdown battle and suggested his colleagues were defeatists.

This is perfect. Not only was Cruz unable for articulating a strategy for winning the fight he insisted the party wage, he also attacked fellow Republicans as defeatists for being angry about it.

Remember, even the House GOP leadership’s own pollster has warned that conservatives have failed to articulate an endgame in this battle, and that a protracted government shutdown is politically untenable. But if conservatives are to blame for the GOP’s current fix, isn’t the way out to stop ministering to their demands and conditions?

This basic disconnect is why the GOP is currently spinning its wheels. Politico reports that John Boehner is now looking towards the debt limit, rather than just the government shutdown, as a way of extracting concessions from Democrats, and adds details about a private meeting:

The speaker told those gathered that changes to Obamacare should be “part” of  the party’s budgetary message, according to those gathered. There is fear inside  leadership that if they don’t talk about the Affordable Care Act, conservative  lawmakers will accuse them of abandoning the party’s pledge to defang the law.  But it’s clear Boehner is aiming beyond Obamacare to entitlements and a rewrite  of the Tax Code.

Look, this is nuts. Boehner realizes Obama is not going to seriously undermine Obamacare in exchange for keeping the government open. So the answer to this is to keep conservatives happy by continuing to vaguely keep the law as part of the discussions, while extracting concessions — on entitlements — in exchange for a debt limit hike? But Democrats aren’t going to agree to those things, either.

This is the crux of the issue. Conservatives don’t have any way out of this predicament, but they won’t allow Republican leaders to find any way out of it that could ever get the support of Democrats or the president, which is of course necessary for it to succeed. Yet GOP leaders continue to look for a way out that will keep conservatives happy, or at least not anger them too much. Now perhaps it’s true that Boehner can’t alienate conservatives without weakening himself fatally. But we should be clear here that if this is going to shape the party’s continued strategy, the stalemate — which even some Republicans believe is far worse for the GOP than for Obama — will only continue, with default looming.

* A SIMPLE WAY OUT FOR REPUBLICANS: Related to the above, the Hill reports that House Republicans are growing increasingly restless about the GOP strategy, and adds this deceptively simple observation:

While many rank-and-file Republicans are showing much less appetite for breaching the debt ceiling than they did in 2011, GOP lawmakers argue they have other leverage points — like sequestration — to bring Democrats to the table.

Bingo! Sequestration is what Republicans should use for leverage! In other words, open the government and raise the debt ceiling for the good of the country, and enter into normal long term budget talks!

* THERE ARE A LOT OF UNINSURED IN RED STATES: Ronald Brownstein has a terrific look at the demographics of Obamacare, finding that the increased coverage of the uninsured would carry almost as many benefits for residents of GOP House districts as it would for Democratic ones:

Recently released census data show that, on average, the share of residents without insurance is almost as high in districts represented by House Republicans as in those represented by Democrats…This dynamic underscores how thoroughly ideology is trumping interest as Republicans convert the budget and debt showdowns into their Thermopylae for blocking Obamacare. Because so many House Republicans represent districts with low coverage levels, these members are effectively seeking to prevent a substantial flow of federal dollars not only to uninsured individuals in their communities but also to hospitals, doctors, and other providers who now are delivering significant levels of uncompensated care.

This illustrates once again that Republicans are actively trying to prevent Obamacare’s benefits from reaching their own constituents, and that over time, as the ideological fervor against Obamacare wanes, GOP lawmakers might become more motivated by what’s in the interests of health care institutions in their districts.

* MORE RED FLAGS FOR GOP: New polling released by CBS News finds that 61 percent of Americans — and 84 percent of independents — think Republicans are opposing Obama policies to gain political advantage, rather than over substantive policy disagreement. Far fewer think the same of Dems. While 51 percent disapprove of Obamacare, 20 percent think the law doesn’t go far enough, while only 43 percent say it goes too far.

Opinion on Obamacare is more nuanced than Republicans suggest; and Republicans in the shutdown fight are burdened with an image as far more uncompromising and uninterested in constructive governing.

* BUT CONSERVATIVES THINK THEY’RE WINNING, ANYWAY: A crucial point from MSNBC’s First Read crew (no link yet):

One of the major differences between the last shutdown (in 1995-1996) and now is the rise of FOX News, Drudge, and Breitbart News. As the New York Times recently wrote, “a fervent group of conservatives — bloggers, pundits, activists and even members of Congress — is harnessing the power of the Internet, determined to tell the story of the current budget showdown on its terms.” It explains why conservatives aren’t as convinced as many others are that this will do significant damage to the party.

Yep. The perils of the closed conservative information feedback loop at work.

 * REPUBLICANS WORRY OBAMACARE IS GOING TO WORK: Paul Krugman’s column today argues that Republican officials don’t really know why they are even shutting down the government, and are not motivated by any substantive policy goals on health care, other than a nagging fear that Obamacare is going to work. And don’t worry about those glitches:

Because they appear, for the most part, to be the result of the sheer volume of traffic, which has been much heavier than expected. And this means that one big worry of Obamacare supporters — that not enough people knew about the program, so that many eligible Americans would fail to sign up — is receding fast.

 * OBAMA HAS OPTIONS TO AVERT DEBT LIMIT CRISIS: Adam Liptak has a nice dive into the legal scholarship around whether Obama has ways of averting default unilaterally if he decides to exercise the executive authority to do so. As it happens, though, Obama officials are still ruling out any of these options. As I reported yesterday, the White House believes a decisive defeat of the GOP in this battle — one that breaks the addiction to using the threat of default as leverage once and for all. — is imperative.

* AND ANOTHER POLL SHOWS DE BLASIO SOARING: A new New York Times poll finds progressive Bill de Blasio leading Republican Joe Lhota by 68-19 in New York. Voters support de Blasio’s plan to expand pre-K education and fund it with tax hikes on the wealthy by almost three to one. That’s one of the proposal liberals are watching for a sign of whether newly aggressive policies to combat inequality can help steer the Democratic Party in a more economically progressive direction.

What else?