WASHINGTON – A day after their vote to repeal President Barack Obama's landmark health care law, House Republicans moved Thursday to put their own stamp on the issue, starting with the volatile topic of abortion.

The highly charged issue nearly scuttled passage of the health care law last year. The move to reopen that debate is part of an emerging GOP strategy to attack in the health care law piece-by-piece and promote ideas of their own.

It could also drive a wedge between the majority of Democratic lawmakers who support abortion rights, and a smaller group of abortion opponents within their ranks who signed on to the compromise, thereby providing the critical margin to pass the overhaul last year.

GOP lawmakers introduced two separate bills to toughen restrictions on taxpayer funding of abortions, arguing that the language now in the law is weak. Leaders promised swift action.

Clearly there's an awful lot of doubt as to where the administration really is on this issue," said House Speaker John Boehner, R-Ohio, calling the abortion legislation one of his top priorities. "I think the will of the people is that we enact this clear-cut prohibition on the use of taxpayer funds for elective abortions.

The tree is rotten, so you have to cut it down," said Ways and Means Chairman Dave Camp, R-Mich. "If we can't do that all at once, prune it branch by branch.

Among other health care issues getting immediate attention from Republicans: curbs on jury awards in medical malpractice cases, rescinding an unpopular requirement that businesses report purchases of $600 or more to the IRS, and a rollback of cuts to private Medicare Advantage plans.

On Thursday the House voted 253-175 along party lines to instruct committees to begin the work of replacing what Republicans dismiss as "Obamacare.

The GOP move on abortion puts ideology ahead of pocketbook issues, said Rep. Rosa DeLauro, D-Conn., a leader on women's rights.

These are folks who came to town saying they'd create jobs and get the economy back on track," DeLauro said of the new Republican majority. "This legislation goes far beyond current law. Given the opportunity to govern, they are once again trying to deny women's access to abortion.

Federal law prohibits federal funding for abortion, except in cases of rape, incest or to save the life of the mother. Known as the Hyde amendment, that basic prohibition is incorporated in many laws and generally has to be renewed annually in spending bills.

The health care law created a new stream of federal funding for health care: tax credits to subsidize private insurance coverage for people participating in new state marketplaces called "exchanges." They open for business in 2014.

Since abortion is widely covered by private insurers, advocates on both sides of the issue mobilized.

Abortion opponents sought to impose the Hyde amendment on plans offering coverage through the exchanges. Abortion rights supporters said that would have the effect of taking away access to a legal medical procedure now available to privately insured women.

The law struck a compromise that divided abortion opponents and displeased most abortion rights supporters. It allowed plans in the exchanges to cover abortions, provided they collect a separate premium from policy holders and that money is kept apart from federal subsidies received by the plans.

It also allowed individual states to ban abortion coverage in their exchanges, and provided that there would be at least one plan in every state that does not cover abortions. Obama issued an executive order reaffirming longstanding restrictions on abortion coverage.

Nonetheless, many abortion opponents saw a backdoor opening. "We are setting up a funding scheme to pay for abortions," said Rep. Chris Smith, R-N.J., sponsor of one of the two bills introduced Thursday.

Both bills would forbid plans in the exchanges from covering abortions. However, women could purchase a separate policy to cover the procedure.

Smith's legislation would make the Hyde amendment permanent and apply it across all government programs.

A separate measure, by Reps. Joe Pitts, R-Pa. and Dan Lipinski, D-Ill., would apply the Hyde restrictions to the new health care law. Energy and Commerce Chairman Fred Upton, R-Mich., said it would get priority consideration.

Like the overall GOP push for repeal, the abortion curbs seem headed for a dead end in the Democratic-led Senate. Majority Leader Harry Reid, D-Nev., has said he'll block efforts to repeal the overhaul, or unravel it.

Whatever Republicans do, Democrats say they're confident the public will ultimately conclude it doesn't measure up to the law already on the books, an expansion of society's safety net sought by Democratic presidents going back to Harry Truman.

It would expand coverage to more than 30 million uninsured people, reduce costs for Medicare recipients with high prescription drug bills and bar insurers from denying coverage to people with health problems. Starting in 2014, most Americans would be required to have health insurance. Millions of middle-class households would be able to purchase a plan through new state-based insurance pools, with tax credits to make premiums more affordable.

Four committees — Ways and Means, Energy and Commerce, Education and Workforce, and Judiciary — have been instructed to work out the Republican vision for health care. Leaders, working on the assumption that the repeal bill will not become law, have set no timeline. The prospect is for months of maneuvering.

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Associated Press writer Larry Margasak contributed to this report.