Specifically, the bill would prohibit people from deducting medical expenses on their taxes related to abortion costs. The bill would also ban tax credits for companies that offer health plans that include abortion coverage.

Democrats said these provisions are a significant intrusion into the privacy of U.S. citizens, and said they would have the effect of preventing women from making a legal choice to have an abortion.

"The right to choose is absolutely meaningless without access to choice, and H.R. 3 creates obstacles for women to access safe, legal and constitutionally protected healthcare," Rep. Carolyn Maloney (D-N.Y.) said. "This makes access to abortion coverage incredibly difficult."

Democrats also argued that report language for the bill makes it clear that Republicans want to prevent federal funding for abortions in the case of statutory rape. Report language cited by Rep. Louise Slaughter (D-N.Y.) reads as follows:

"Reverting to the original Hyde Amendment language should not change longstanding policy. H.R. 3, with the Hyde Amendment language, will still appropriately not allow the Federal Government to subsidize abortions in cases of statutory rape."

Republicans insisted that the bill is only meant to ensure that tax dollars are not used for elective abortions, and said this reflects a growing consensus in the country.

"America has changed, and today is more pro-life than ever," said Rep. Chris Smith (R-N.J.), the author of the bill.

Comments on the bill Wednesday afternoon were made in the context of debating the rule for the bill, which the House approved in a 243-177 vote. Twelve Democrats voted in favor of the rule.

President Obama has said he would veto the bill if it were presented for his signature, although the Senate is not expected to take up the bill.

-- This story was updated at 1:57 p.m.