In this March 23, 2010 file photo President Barack Obama signs the health care bill in the East Room of the White House in Washington. (J. Scott Applewhite/AP)

More than a year after Republicans first pledged to “repeal and replace” President Obama’s new health-care law, the GOP is still struggling to answer a basic question.

Replace it . . . with what?

The repeal-and-replace argument has been a central line of attack in the GOP’s anti-Obama assault, both on the presidential campaign trail and on Capitol Hill.

In Congress, the new Republican-led House took a symbolic vote to repeal the law in January. But since then, nothing has happened. The House hasn’t passed anything new to take its place.

On the campaign trail, both former House speaker Newt Gingrich (Ga.) and former Massachusetts governor Mitt Romney have said they want to repeal the law.

To replace it, they have reused several ideas from 2008 GOP nominee John McCain. Instead of a mandate to buy insurance, the two current front-runners would offer ways to make insurance cheaper: new tax credits, new bargains on policies from out-of-state.

But even some conservatives say these ideas might not work as advertised. And they would only be the beginning of a true “replacement” for Obama’s sweeping law.

With the 2012 elections less than a year away, Republicans’ struggle over health care could be a political liability. Democrats will blast them for breaking a promise.

It could be even more of a problem after the election. If the GOP can repeal the law, it would reopen the ugliest political fight of the past five years.

But the GOP wouldn’t have a plan to win it.

“If Republicans aren’t talking about how they would replace Obamacare,” said Michael Cannon, the libertarian Cato Institute’s director of health policy studies, “there are two good reasons for that.”

“The first one is: They’re winning the argument. Why would they change the subject?” Cannon said, meaning that Republicans have won support by focusing only on the “repeal” part of their promise. “The second one is: Their current proposals [for replacement] aren’t ready for prime time.”

Obama’s health-care law stretches over hundreds of pages, making a sweeping attempt to solve two long-standing problems. One was the millions of uninsured people. The other was the fast-rising cost of medical care.

To address the first, the law simply mandated that every American buy health insurance. If not, people could face a fine of $695 or more. To address the second, the bill drives hospitals — especially those treating Medicare patients — toward more efficient treatments.

To Republicans, the law looked like a jury-rigged mess, tainted by special favors and bloated government. They attacked the “individual mandate” as federal over-reaching, and the efficiency efforts as a first step toward the rationing of medical care.

It worked, and it is still working.

Last fall, the GOP won a whopping 63 new House seats. This year, Republicans are still campaigning to repeal the law, which a recent poll showed is viewed unfavorably by 44 percent of Americans (and favorably by only 37 percent).

But, at the same time, the GOP promised to unveil its own solutions to the same problems.

“We can do better. We can do better than their government takeover of health care,” Rep. Mike Pence (R-Ind.) said in January, when all 242 House Republicans and three Democrats voted to repeal the law. That repeal measure stalled, as expected, in the Democrat-held Senate. “It all begins with today,” Pence said.

In the House, however, not much has happened since.

Some Republican members have sketched out their own plans. One would let people take their health insurance with them from job to job. Another limits the damages handed out in malpractice suits. Another would let people get insurance through private associations, not just their employers.

But none has been passed.

“Thus far, the relevant committees have been focused on oversight to protect the American people from the effects of the law, and repeal,” Michael Steel, a spokesman for House Speaker John A. Boehner (R-Ohio), said in an e-mail. “I expect we will see more ‘replace’ efforts in the coming year.”

On the campaign trail, the two GOP front-runners are men who have both embraced the hated “individual mandate” in the past. But now, both Gingrich and Romney say they would repeal the bill if they could.

“I think it’s incumbent on everybody around this table to put together a plan that says, ‘This is what I’ll replace it with,’ ” Romney said in a debate in October. “Because the American people are not satisfied with the status quo.”

In many ways, these two bitter rivals have proposed similar ideas.

One shared idea, borrowed from McCain, is to replace a stick with a carrot. Instead of fining people who don’t buy insurance, they would reward tax breaks to those who do. If insurance is cheap enough, the logic goes, the uninsured will buy a policy without being forced to.

But what about people who don’t get the hint and remain uninsured? Romney would allot each state a pool of taxpayer money to provide for their care.

Gingrich has another solution — tinged with the former speaker’s affinity for complex systems.

He envisions a system in which the government puts aside the tax breaks that a particular uninsured person would have received. The taxpayer money would then be sent to his or her local community to pay the doctor bills if the person gets sick.

“You don’t want to buy the insurance? Fine,” Gingrich explained on CNN this month. “Your share of the tax credit goes into a charity pool. Something happens to you, you’re taken care of by that charity pool.”

In addition, both Gingrich and Romney want to allow insurance to be sold more freely across state lines. The logic is that a Marylander, for instance, might find a cheaper plan from an insurer in another state that doesn’t set such strict rules on insurers.

But this idea attacks a notion that both Gingrich and Romney profess to love: the sovereignty of states. It strips away the ability to limit the insurance sold within their borders, a power many states are loath to give up.

Some conservatives worry that this will create an opening for more federal regulation of the interstate insurance market. But Romney said that wouldn’t happen.

If a state’s insurers got out of control, the states’ residents could solve the problem by themselves.

“The people of that state are going to vote out of office the people that don’t do a good job,” he said at a speech in May.

Romney has also said he would do away with the Obama plan’s rule that prevents companies from denying coverage for “preexisting” conditions. Romney would offer that guarantee only to people who have maintained continuous health insurance — not those who are without it. Gingrich’s plan does not offer that guarantee: He proposes expanding state “high-risk” coverage plans that people with preexisting conditions could buy.

For now, the two front-runners’ ideas have left some in the Republican Party wanting more.

“They’re a step in the right direction. However, I don’t believe that they are fundamental reform,” said Rep. Tom Price (R-Ga.), author of one of the reform bills in Congress. “They don’t go broadly enough, to change the health financing and delivery system.”

But others can see the political logic. As Democrats learned, changing health care means dealing with a series of volcanic issues: fairness, malpractice, the proper role of government. And life and death.

If “repeal” is enough for the GOP primary, they said, then the details of “replace” should wait until later.

“You don’t want to be terribly detailed,” said Rep. Michael C. Burgess (R-Tex.), who advised McCain in his presidential run, and saw the details of his ideas turned into weapons by Obama. “It’s a whole lot easier to demagogue the ‘con’ than it is to defend the ‘pro.’ ”

Polling manager Peyton M. Craighill contributed to this report.