Feb. 8, 2011 -- For more than 30 years, both sides of the U.S. abortion debate have agreed that no taxpayer dollars should be used to fund the procedure, except in instances of rape, incest and when the life of the mother is in danger.

The legal underpinning of the agreement, known as the Hyde Amendment, has been attached to appropriations bills for federally-funded health services, including Medicaid, every year since 1976.

Now House Republicans want to make those restrictions tighter -- and permanent -- with several new pieces of legislation meant to ensure no federal funds even indirectly support abortions performed nationwide.

The "No Taxpayer Funding for Abortion Act," debated Tuesday before a panel of lawmakers on Capitol Hill, would formally codify the Hyde Amendment, creating what supporters call a clear and consistent national policy.

The bill would affirm an existing "conscience clause," allowing hospital employees and other health care providers to refuse to perform abortions if they believe the practice violates their moral or religious beliefs.

The legislation would also create new prohibitions on tax credits for corporate and individual health care plans that include abortion coverage, even if the purchaser does not receive or intend to receive an abortion.

"This bill will not be a departure from decades of implementation of the Hyde Amendment policy," said Rep. Trent Franks, R-Ariz., one of 173 Republican co-sponsors of the bill.

But many Democrats disagree, arguing the bill amounts to a direct attack on the constitutional rights of women, as upheld by the Supreme Court in Roe v. Wade, and an unfair financial burden on women who buy their own health plans.

"This has very little to do with taxpayer funding for abortion and places government in the middle of private health care choices telling businesses and individuals how they spend health care dollars," said Rep. Jerrold Nadler, D-N.Y., who warned the bill would amount to a tax increase on women who buy insurance that provide for abortions.

An earlier version of the measure, first introduced by Rep. Chris Smith, R-N.J., had sought to redefine rape for purposes of exemption of the funding ban under the Hyde Amendment -- drawing sharp criticism from women's rights groups and Democrats.

The language would have allowed for subsidized abortions only in cases of "forcible rape," and limited exempt cases of incest to only those involving minors.

"To suggest that rape of any kind is acceptable -- to suggest that the only time that a woman could get coverage for a resulting pregnancy would be when she was forcibly raped, as if some other kinds of rape are okay, is outrageous," said Rep. Debbie Wasserman Schultz, D-Fla.

House Republicans have since promised to drop the change to the rape language.

With a Democratic majority in the Senate and President Obama in the White House, the measures are not likely to become law. But Republican leadership and House Speaker John Boehner have called the bill a "top legislative priority."

House GOP Makes Abortion Priority

House Republicans plan additional hearings on other abortion legislation in the weeks ahead.

Rep. Joe Pitts, R-Pa., has introduced the "Protect Life Act" which would impose additional restrictions on taxpayer-subsidized insurance plans that will be available as part of the new health care law.

The law already stipulates that women who are eligible for the plans and want abortion coverage must purchase that provision separately, with their own funds. Pitts' bill would clarify the process and require, among other things, that insurance providers offer an abortion coverage-free plan.

Rep. Mike Pence, R-Ind., has introduced the "Title X Abortion Provider Prohibition Act" which would curtail federal family planning grants for groups like Planned Parenthood, which provides abortion services and receives more than $350 million in federal dollars each year.

"The largest abortion provider in America should not also be the largest recipient of federal funding under Title X," Pence said last month. The bill "will prevent any family planning funds under Title X from going to Planned Parenthood or other organizations that perform abortions. It will ensure that abortion providers are not being subsidized with federal tax dollars."

Democrats have vowed to fight the measures and accused Republicans of violating their promise to focus on jobs and the economy.

"They're focusing on extreme legislation that takes away women's ability to make their own reproductive life decisions and choices," said Schultz. "This is severe and dangerous legislation and the fact that the Republican leadership is making it a priority … shows that they are more interested in highjacking a woman's independence over her own body rather than focusing on our nation's No. 1 priority: jobs."

ABC News' Huma Khan contributed to this report.