WASHINGTON – With the House preparing to vote this week on whether to repeal the health care law, the chamber’s new Republican majority already confronts a far more delicate task: forging its own path to expand health coverage and curb medical costs.

The House’s GOP leaders have made clear that they regard the repeal vote, scheduled to begin Tuesday, as the prelude to a two-prong strategy that is likely to last throughout the year.

They intend to dismember the sprawling law, pushed through Congress by Democrats last year, by individual pieces before major aspects of it go into effect. At the same time, Republicans say, they will construct their own plans to revise the health care system.

On the cusp of undertaking this work, the GOP has a cupboard of health care ideas, most going back a decade or more. They include tax credits to help Americans afford insurance, limiting awards in medical malpractice cases and unfettering consumers from rules that require them to buy insurance policies regulated by their states.

In broad strokes, the approach favors the marketplace over government programs and rules.

House Republicans have termed their strategy “repeal and replace.” But according to GOP House leaders, senior aides and conservative health policy specialists, Republicans have not yet distilled their thinking into a coherent plan.

“Replacing Obamacare is not something we can accomplish overnight,” said the new House Energy and Commerce Committee chairman, Rep. Fred Upton, R-Mich., using the GOP pejorative for the new law. “We want to get it right, and on complex issues like these with huge consequences for the economy and jobs and spending, that means it may take time. But mark my words, we will get this done.”

In the absence of a plan, Republican leaders nevertheless are eager to convey that they have ideas about health care — and are not merely trying to knock down those of the Democrats.

As a result, they have drafted a resolution to accompany the repeal legislation. It lays out broad, long-held GOP health care goals, but no specifics, and directs four House committees to develop legislative proposals.

Even Democrats acknowledge that the GOP has enough votes to pass the repeal measure and the resolution.

But there is no evidence those quick Republican victories will spill over into the Senate, where Democrats remain in the majority. And President Obama, for whom health care reform is a major accomplishment, will be in office at least two more years.

House committees plan to conduct hearings both to single out parts of the new law for criticism — starting within weeks with those pieces they say could harm jobs — and to develop their own proposals.

A particular challenge for Republicans will be the possible effect of removing the law’s requirement, as they have vowed to do, that most Americans carry health insurance starting in 2014, according to Mark D. McClellan, director of the Brookings Institution’s Engelberg Center for Health Care Reform, who held several senior health-care positions in the Bush administration.

He said the GOP will need to be careful to put in other means to deter people from drifting in and out of the insurance market, depending on whether they need care.

A few parts of a GOP proposal drafted in 2009 overlap with provisions of the new law. Among them are high-risk pools — special insurance for Americans rejected by insurance companies because they already are sick.

Like the new law, the GOP version also would have allowed young adults to remain longer on their parents’ policies and would have tried to give consumers more information to use in choosing insurance. “Some of the ideas . . . are not intrinsically Republican or Democratic,” said Douglas Besharov, a public policy professor at the University of Maryland. “It’s their implementation that’s left or right.”

Other elements of the 2009 GOP proposal would have been major departures from the new law. It would have let people buy insurance across state lines — a darling of conservative policy thought. The idea is to help drive down insurance prices by giving people access to less generous and less costly insurance policies sold in states that mandate fewer required medical benefits.

The Republican plan also would have expanded the use of “health savings accounts,” another approach long favored by conservatives that lets people set aside money for future medical expenses on a tax-free basis, in combination with bare-bones insurance policies.