It's the middle of the night in New Hampshire, and a teenager, afraid to tell her parents she is pregnant, appears at an emergency room. A doctor diagnoses a spike in blood pressure that won't kill the girl but could render her sterile unless she has an immediate abortion. The doctor calls a judge for permission to perform the procedure, as state law prescribes -- and voice mail answers.

"What's supposed to happen?" asked Justice Stephen G. Breyer, who posed the hypothetical situation during oral arguments at the Supreme Court yesterday.

The dilemma, probably rare but undeniably dramatic, defines the most significant case on abortion rights to reach the court in half a decade. The basic right to abortion, recognized by the court 32 years ago in Roe v. Wade, is not at stake, but the scope of the right may be.

The New Hampshire parental notification law, passed in 2003, requires minors to tell a parent before they can get an abortion, unless a judge grants a "bypass." The only stated exception is for girls who would die without an abortion. A Boston-based federal appeals court ruled that the lack of an express health exception made the entire statute too restrictive and declared it unconstitutional.

New Hampshire appealed to the Supreme Court, arguing that the court's past abortion rights decisions do not require a health exception. A broad decision in the state's favor could clear the way for other states to enact similar statutes, and bolster the Bush administration's legal argument for the federal ban on the late-term procedure called "partial birth" abortion by opponents. The administration backs New Hampshire in the case, Ayotte v. Planned Parenthood of Northern New England, No. 04-1144.

But at yesterday's argument, the justices appeared to be probing instead for a compromise solution, one that might give New Hampshire a chance to preserve its law for the vast majority of cases, while giving physicians and teenage patients a way out of the problem Breyer's question summarized.

Leading the search for a middle ground was the court's newest member, Chief Justice John G. Roberts Jr., who repeatedly suggested that the court could send the case back to lower courts for a narrower challenge to the law as it applies to emergencies such as the one Breyer outlined.

"Presumably the litigation would be very similar to what we've seen in this case," he told a lawyer representing Planned Parenthood of Northern New England, "but it would be focused on the provision that is causing you concern, rather than the statute as a whole."

The lawyer, Jennifer Dalven of the American Civil Liberties Union, urged the court to uphold the appeals court's invalidation of the entire New Hampshire law and leave it to the state legislature to make any changes.

"If this court rewrites it," she said, "it will give a green light to legislatures around the country to pass broad restrictions, and leave it to women and doctors to go to court and be the sole defenders of the right."

Most states have parental involvement laws relating to abortion, but New Hampshire is one of only five that does not include a health exception.

In answer to Breyer's question, New Hampshire attorney general Kelly A. Ayotte said that doctors confronted with a midnight emergency could proceed, protected by other provisions of New Hampshire law that shield doctors' good-faith medical decisions from liability.

But Breyer said the parental notification law itself "suggests the contrary." He also did not embrace Roberts's approach, telling U.S. Solicitor General Paul D. Clement that any effort to have courts craft a solution would "get into the greatest difficult issue there is in this area, which is: What does that health exception mean? We've said throughout that that health exception has to be defined first by a legislature."

But two key moderates on the court -- Justices Sandra Day O'Connor and Anthony M. Kennedy -- made comments similar to Roberts's. And one of the court's more liberal members, Ruth Bader Ginsburg, while generally voicing skepticism about New Hampshire's position, implied late in the argument that she might be open to a compromise.

Ginsburg sketched a hypothetical option like the one offered by Roberts, then observed to Dalven: "Then you would have no complaints about the rest of the statute."

It was expected that the case would not turn into a vehicle for reassessing Roe v. Wade. But the repeated emphasis on a narrow ruling that might return the hardest questions to lower courts was perhaps more of a surprise.

New Hampshire had not only asked the court to rule that it does not have to have a health exception, but it also asked the court to apply a strict standard under which its law could not be challenged unless it could be shown to be unconstitutional in all circumstances.

At yesterday's argument, however, the justices showed little interest in that claim. And Ayotte and Clement readily agreed when asked whether they would be satisfied with a ruling that narrowed the issue to emergency cases and sent the matter back to the lower courts.

"We think that is a very good mechanism," Ayotte told Roberts.

"The entire tenor of the justices' questions suggested that they are focused upon the specifics of the New Hampshire case and not any broader questions," said David J. Garrow, an abortion-law specialist at Cambridge University in Britain, who attended the argument.

Attorney General Kelly A. Ayotte, center, offers reactions after arguing New Hampshire's side of the case involving its 2003 law requiring minors to notify parents before they can get an abortion. The law has a judicial "bypass" clause.