(CNN) -- Overriding a veto by Arkansas' Democratic governor, the state's Republican-controlled House and Senate approved a bill to ban abortions after 12 weeks of pregnancy -- the most restrictive such law in the country.

Gov. Mike Beebe, a Democrat, vetoed the bill Monday, saying it "blatantly contradicts the United States Constitution, as interpreted by the Supreme Court."

But on Wednesday, the Arkansas House voted 56-33 to override the veto, following a 20-14 override vote a day earlier in the state Senate.

The Center for Reproductive Rights and the ACLU of Arkansas promised to mount a legal challenge in federal court, while supporters said they were prepared to fight back.

"We intend to make it ... clear that no one's constitutional rights are subject to revision by lawmakers intent on scoring political points, and that attempts such as this to turn back the clock on reproductive rights will not stand," Nancy Northup, president and CEO of the Center for Reproductive Rights, said in a statement.

Should the state lose the challenge, it will have to pay all the legal fees in the case.

But Rep. Ann Clemmer, a Republican supporter, says the money would be well spent.

"Protecting unborn children is ... an important way to spend state resources," she told CNN affiliate KATV in Little Rock.

Called the "Arkansas Human Heartbeat Protection Act," the bill requires testing to determine "whether the fetus that the pregnant woman is carrying possesses a detectible heartbeat."

Abortions would be banned if the fetus has a detected heartbeat "and is under 12 weeks or greater gestation."

Roe v. Wade, a 1973 decision by the U.S. Supreme Court, legalized the right to an abortion in all 50 states. Statutory time limits on when abortions can take place, however, vary from state to state. Some states have no time limit, while others allow abortion up to the end of the second trimester -- about 27 or 28 weeks into the pregnancy.

Two women's stories

As is so often the case with this issue, there are deep divides.

Kandi Cox, who had an abortion 20 years ago when she was 19, now heads Abba Adoption, an agency that offers support for women and teens who choose adoption rather than abortion for their unborn child.

"This is a day of celebration within our state, where we can say that we as the state of Arkansas, we stand for life," Cox told CNN affiliate KARK-TV. "We're going to continue to fight until Arkansas stays a solid state for life."

But Jan Gerber, who also had an abortion, said she has no regrets about her decision to end her pregnancy.

She is a registered nurse, who signed a petition by Physicians for Reproductive Choice and Health to support abortion providers.

"I stand for choice," Gerber told KARK. "I stand for the little girl who thinks her voice has been taken away from her, and I'm 60 and I'm older and I want to say to that little girl, 'you do have a choice.'"

CNN's Darrell Calhoun and Joe Sutton contributed to this report