But so far, more radical measures elsewhere have fallen short. In Mississippi a so-called personhood amendment lost at the polls, while in Ohio a “fetal heartbeat” bill resembling that in Arkansas was defeated in the legislature, in part because it was opposed by one of the state’s leading anti-abortion groups, Ohio Right to Life.

Those proposals have caused soul-searching and dissension within some of the largest anti-abortion groups, with many traditional leaders expressing skepticism or opposition to such sweeping challenges to constitutional law until a more conservative Supreme Court seems ready to scrap the legacy of Roe v. Wade.

Much like Tea Party activists, who have caused exasperation among Republican leaders with demands to slash budgets almost indiscriminately, the abortion rebels feel there is little to lose by pushing for aggressive curbs and testing the courts. But other anti-abortion leaders say that strategy, exemplified by the Arkansas law, is likely to backfire, causing courts to endorse the current limits and wasting resources that could bring real, if smaller, gains.

“As much as we would like to protect the unborn at that point, it is futile and it won’t save any babies,” said James Bopp Jr., a prominent anti-abortion lawyer who opposed the Arkansas law. Mr. Bopp, who lives in Indiana, is general counsel of National Right to Life.

He said that lower courts are virtually certain to affirm existing Supreme Court rulings and, like many other legal experts, he predicted that the Supreme Court was very unlikely to agree to hear such a case.

Mr. Rapert originally proposed setting the Arkansas ban even earlier, at about six weeks after a woman’s last menstrual period. But the nascent fetal heartbeat can be detected at that point only by using intrusive technology like a trans-vaginal ultrasound.

Wary of the national firestorm that erupted last year after Virginia tried to require the intrusive procedure, Mr. Rapert and his allies revised the bill to specify that a fetal heartbeat should be detected by abdominal ultrasound or other external methods, which are not feasible at six weeks.