More than four years after initiating an all-out war to block — and then destroy — what they derisively labeled “Obamacare,” Republican leaders remain at a loss on how they’d replace the law if their dream of repealing it should ever come true.

Even as conservative health wonks plead with their party to get serious about an alternative, the GOP’s headlong pursuit of its Obamacare whale is narrowing its already scant options in devising a bill that fixes the glaring market failures in the system and can satisfy its base. “Repeal and replace,” as the slogan went, has effectively morphed into “repeal … and then we’ll consider doing something but we’re not sure what.”

This paradox was on display during the Sunday talk shows when Sen. Kelly Ayotte (NH), an ambitious first-term Republican who is close to leadership, lambasted Obamacare as a “mess” but struggled to explain what she would support as an alternative.

“Well, I would say let’s get to the table on a bipartisan basis and let’s make sure that we have a plan that has more choice, not less,” she said. “Let’s have one where we’re driving down costs and increasing competition. Have the insurance companies compete in a way that they aren’t right now.”

So … what does that mean?

“Let’s get together and figure out what are the best models from the state law on the high-risk pools to address preexisting conditions. There are many ideas I think that we could do that won’t harm people who have policies now that they would like to keep,” Ayotte said. “We should work together to address this health care reform instead of the way this was done on party lines.”

The one idea Ayotte invoked, state-based high-risk pools, is something Republican leaders frequently point to when asked how they’d help people with preexisting conditions. But it has major conceptual and political flaws. Subsidizing care for the sickest individuals is very expensive; as a result, these pools are dramatically under-funded in the states that have them, and therefore fail to cover millions of people.

The political problem is congressional Republicans don’t want to spend anywhere near the kind of money necessary to make this work. Conservative health experts James Capretta and Tom Miller estimated in a 2010 paper that functional high-risk pools would cost some $15-$20 billion per year and cover up to four million people.

Earlier this spring, House conservatives scuttled a bill by Majority Leader Eric Cantor (R-VA) to spend a total of $3.6 billion (financed by cutting Obamacare) on high-risk pools. The bill was a messaging device to boost the GOP’s credibility with sick people, and Cantor, facing strong conservative opposition, yanked it at the last minute. His office told TPM it would try again in May. It’s now November, and the bill hasn’t been brought back.

“Subsidizing health care is not what Republicans should be about,” Rep. Raul Labrador (R-ID) told reporters at the time.

There are several other ideas Republican leaders float when pressed to explain their Obamacare alternatives. Two weeks ago, No. 2 Republican Sen. John Cornyn (TX) said “some of the alternatives” his party has offered include equalizing the tax treatment of employer-provided and individually purchased insurance and letting people buy policies across state lines.

There’s a conspicuous problem with these proposals: they’d arguably be more disruptive to the status quo than Obamacare and likely force many people to lose their insurance plans. That’s an implicitly difficult political proposition, but especially now that the GOP is raising hell about insurance cancellations due to new rules established by Obamacare.

Equalizing the tax treatment of health insurance means unwinding the tax exclusion for employer-provided insurance, which has policy benefits but would disrupt a central pillar of the health care system. As a result, it faces strong bipartisan opposition in Congress. Rep. Paul Ryan (R-WI) originally supported the idea but omitted it from his budget blueprints; one of his top aides lamented to this reporter in 2011 that it had been “falsely framed as a tax increase.”

Experts say that allowing people to buy insurance from other states would initiate an exodus among insurers from states with heavy regulations to states with the fewest regulations, setting in motion a spiral that stands to end millions of existing policies. It would render useless efforts by some states (and the Affordable Care Act) to establish minimum benefit standards, as insurers could relocate to less-regulated states to dodge those regulations and still be able to sell plans to anyone in the country.

“We believe that we can replace Obamacare with reforms that will make it easier for people to acquire or keep a health insurance plan that meets their actual individual needs. My friends across the aisle continue to say we haven’t offered a practical alternative, but that’s just not true,” Cornyn said on the Senate floor. He hasn’t introduced or supported a bill that would achieve these goals, likely because writing such legislation would mean that the Congressional Budget Office would analyze it. Such an analysis would highlight the costs and number of people who stand to lose coverage, which risks invalidating the GOP’s premise that Obamacare is worse — or more disruptive — than an alternative.

A Senate GOP health aide acknowledged the party’s “replace” predicament on Obamacare.

“If the question is ‘What is your plan to replace Obamacare with a bill that maximizes coverage?’ we will fail. Period,” said the aide, who was granted anonymity to speak candidly. “If the question is re-framed as ‘What concrete steps can you take to lower cost and increase access?’ we can play. By definition we have no credibility on the former.”

The GOP health care bills out there — offered by lawmakers like Rep. Tom Price (R-GA) and Sen. Tom Coburn (R-OK) — enjoy little GOP support. Price’s bill, which includes tort reform, high risk pools, refundable tax credits and other reforms, has been repeatedly introduced since 2009 but hasn’t gotten a vote in the Republican-controlled House. The Ryan budget, the only consensus GOP proposal to reform health care, reforms government programs like Medicare and Medicaid but largely returns the private health insurance system to the pre-Obamacare status quo upon wiping out the law’s subsidies and mandates.

Conservative health wonks Ramesh Ponnuru and Yuval Levin last week urged Republicans to take up ideas like high-risk pools and reforming the employer-provided insurance tax exclusion. They warned the party that simply repealing Obamacare is untenable and there may be “lurch to the left” — toward single payer — if the law fails.

“What Republicans can and should do is offer the public something better,” they wrote in the Wall Street Journal. “Some Republicans think that political success requires nothing more than watching ObamaCare fail. But if the new system quickly implodes, that would be all the more reason to have an alternative on hand — other than another leftward move toward single payer. And it might not implode so quickly.”