The mandated discussion of fetal heartbeats is one of a cascade of abortion restrictions adopted in Ohio over the years, from a waiting period to curbs on the medication-induced abortions preferred by many women. The pace has quickened since John R. Kasich became governor in 2011, cementing Republican domination of state politics. Avowedly anti-abortion, Mr. Kasich said through a spokesman that he considered the restrictions he signed this year “reasonable.”

These laws have passed without the national drama provoked by far-reaching abortion bans that were approved, then overturned in court, in states like Arkansas and North Dakota. But taken together, they affect patients and clinics in myriad ways — in the view of the laws’ proponents, rightly making women think twice before ending a pregnancy and ensuring clinic safety or, in the view of opponents, imposing heartless obstacles and guilt on women who are seeking a legal procedure.

“In Ohio, the last few years have been fantastic if you support the pro-life movement,” said Mike Gonidakis, the president of Ohio Right to Life. His group has even lobbied against a more sweeping ban on early-term abortions, incurring the wrath of more restless abortion foes. But he says, “We’ve been able to craft pro-life laws that can withstand court scrutiny.”

On Wednesday, the American Civil Liberties Union filed a challenge in state court to the heartbeat mandate and other new restrictions, asserting that they were adopted in violation of the Ohio Constitution’s “single subject” rule because they were part of an unrelated budget bill.

More broadly, abortion-rights advocates call the incremental strategy, which has been refined by several national groups and pursued in a number of states, an insidious way to limit access to abortion and shame women who in many cases already have to walk past shouting protesters to enter clinics.