Despite a wave of late-term abortion restrictions being signed into law in state capitals, advocacy groups like Planned Parenthood so far have held back on filing any legal challenges. 

The hesitation could be a sign that the groups are concerned about their chances in court. The new proposals would ban most abortions after about 20 weeks into pregnancy, narrowing the window in which a woman can seek an abortion, based on claims that a fetus can feel pain after that period. Though these proposals are seen by pro-choice advocates as an assault on reproductive rights, the litigation hasn't started flying. 

Mary Spaulding Balch, state legislation director for the National Right to Life Committee, suggested that's because the momentum is against those groups.

"It would seem to me that they fear a public debate that focuses on the pain of the unborn child," she told FoxNews.com. 

The latest state law to impose these restrictions comes out of Oklahoma. Republican Gov. Mary Fallin on Wednesday afternoon signed a bill, one of two anti-abortion measures, making abortions after the 20-week mark a felony for the doctor. 

Fallin follows governors in Kansas and Idaho who signed similar bills into law last week. Nebraska started the trend with a groundbreaking law passed last year. 

Nearly a dozen other states are considering copycat bills, according to the Guttmacher Institute. Elizabeth Nash, a public policy associate with the abortion-rights institute, said Indiana could be the next state to approve one, and expressed concern that the states are moving so rapidly on the proposals. 

"Our view is that these bills fly in the face of constitutional precedent," she said, referring to standards that typically mark the cutoff for abortions at what's known as fetal viability. Most states with limits on late-term abortions use fetal viability, which is the point when a fetus can survive outside the womb, as the threshold. That can be as early as 24 weeks. 

The laws in Idaho, Kansas, Nebraska and Oklahoma move that up by a month. Only a small percentage of abortions, though, are sought after the 20-week mark. 

The Center for Reproductive Rights has suggested the reason it's not taking to the courts to fight the changes is because they only impact a relatively small number of abortions. 

"They're trying to move the agenda to a small percentage of cases, but we're not fighting on their turf," a CRR official told Politico.com. CRR did not respond to requests for comment from FoxNews.com. 

Planned Parenthood -- which has suffered from a spate of bad publicity after an anti-abortion group released videos purporting to show an actor posing as a pimp soliciting advice from its clinics -- reportedly claims it does not have standing to challenge the latest measures because it doesn't offer late-term abortions in those states. 

Critics of the so-called "fetal pain" provisions nevertheless dispute the science used to justify them. They point to a 2010 study from the Royal College of Obstetricians and Gynecologists which concluded that a fetus "cannot experience pain in any sense" before 24 weeks into a pregnancy. 

"Furthermore, there is increasing evidence that the fetus never experiences a state of true wakefulness in utero," the study said. 

But conservative state lawmakers, who saw their numbers expand after the November elections, are pressing ahead with restrictive measures, particularly in the wake of the 2007 Supreme Court decision which upheld the federal partial-birth abortion ban. 

Balch suggested abortion rights groups are worried that the debate could turn against them if they challenge the latest set of bills in court. 

"While there are people there who have standing to challenge the law, there is a reluctance in the pro-abortion movement to humanize that unborn child," she said. "It's a debate that our opponents do not want to have." 

Balch said her organization is "prepared to go into all the states and pass this law if that's what it takes." 

Most states provide exceptions to consider the life and health of the mother, no matter when the cut-off is set. Nash described those exceptions as limited.