It challenges four decades of constitutional doctrine and is based on disputed scientific theories.

Yet a push to ban abortion at 20 weeks after conception, on the theory that the fetus can feel pain at that point, has emerged as a potent new tactic of the anti-abortion movement. Advocates saw the potential of such a measure because it taps into public concern about late-stage abortions, appears to alter the rules only incrementally, and claims to be rooted in science.

“Any time we talk about developmental landmarks of the unborn child, anything showing that the unborn child is a member of the human family — that gets the public to take a closer look at abortion,” said Mary Spaulding Balch, the state policy director of the National Right to Life Committee, who is widely seen as the architect of 20-week legislation.

The 20-week ban was first adopted in 2010 in Nebraska, where conservatives aimed to rein in one well-known abortion doctor. A pain-based abortion limit has now been enacted in a dozen states, most recently in Texas, and a bill to impose one nationally passed the Republican-controlled House in June. One recent poll, while affirming public support for legal abortion over all, suggested that a majority of people would draw the line at 20 weeks of pregnancy.

Abortion rights advocates call the pain argument duplicitous and say the laws will be declared unconstitutional, arguing that they are a reflection of Republican gains in state legislatures and not a shift in public opinion. But they have also been forced to mobilize against 20-week bills in state after state, and they credit their opponents with effective marketing.