The laws directly conflict with the key threshold set by the Supreme Court: that abortion cannot be banned until the fetus becomes viable. Viability, the ability to survive outside the womb, usually occurs at the 24th week of pregnancy or later, and is determined in individual cases by a doctor, said Elizabeth Nash, a policy analyst in Washington with the Guttmacher Institute, a research group.

The laws have entered into Republican presidential politics. Support for fetal pain legislation is one item in a pledge that anti-abortion groups are asking potential candidates to endorse. Five have signed, but Mitt Romney and Herman Cain have been criticized for refusing to take part in the pledge, which also asks leaders to make opposition to abortion a test for all appointments and to end taxpayer funding of abortion and Planned Parenthood.

“These 20-week laws are absolutely unconstitutional,” said Nancy Northup, president of the Center for Reproductive Rights, a legal group. No one has yet challenged the laws in court, in part because they are so new that few potential plaintiffs have emerged. But advocates for abortion rights are also proceeding warily, fearful that a weak case could end up in the Supreme Court and upend the legal structure established by Roe v. Wade in 1973 and subsequent decisions, with fetal viability as the all-important dividing line between access to abortion and stringent limits.

“We will file a legal challenge when the circumstances and timing are right,” Ms. Northup said.

Ms. Balch and other advocates say they relish a test of the laws in the Supreme Court, where they believe a narrow victory might be possible, changing the terms of the abortion debate for good.

Only 1.5 percent of the 1.21 million abortions each year, or about 18,000, occur later than 20 weeks after conception, and many of these involve medical emergencies, said Ms. Nash of the Guttmacher Institute.