The stakes are significant in the dispute over a New Hampshire law requiring minors to tell a parent before ending a pregnancy, although the case does not challenge the 1973 Roe v. Wade ruling that said abortion is a fundamental constitutional right.
"The case doesn't go to the core of Roe v. Wade; it doesn't ask or require the justices to determine whether the right to an abortion still is a constitutional right," said CBSNews.com legal analyst Andrew Cohen. "It forces the court instead to look again at limits and restrictions and conditions upon that right."
The outcome is likely to signal where the high court is headed on an issue that has been emotional and divisive among the justices and around the country.
"Court dynamics are also in play," reports CBS News correspondent Wyatt Andrews. "The case gets argued in front of Justice Sandra Day O'Connor, one of the architects of the woman's health exception. All sides will be keenly watching to see if O'Connor helps decide this case before the Senate decides if Judge Samuel Alito replaces her."
Abortion was a prominent subject in Roberts' confirmation hearings and has emerged as a major issue in President Bush's nomination of Alito to replace O'Connor, who is retiring. O'Connor has been the swing vote in support of abortion rights.
Abortion cases generally draw large crowds at the Supreme Court, but buzz around Wednesday's argument was particularly frenzied because the court until this fall had no turnover for 11 years.
Abortion rights protesters held signs that said "Save Roe!" while anti-abortion activists sang hymns in front of the court before the argument.
As arguments began, New Hampshire Attorney General Kelly Ayotte urged the court to uphold that state's parental notification law.
Justice David Souter, a New Hampshire native, wasted little time before firing questions at Ayotte about how the state's law deals with situations where a minor's health — but not life — is in danger and she needs an immediate abortion.
Justices Anthony Kennedy and Stephen Breyer zeroed in on how doctors would avoid being prosecuted or sued if they performed an abortion if the minor did not want to notify a parent and a judge was unavailable to provide the necessary approval.
The justices did not seem satisfied when Ayotte said another, existing New Hampshire law would protect the doctor from legal action and that the state's attorney general would set a policy that would shield physicians in such instances.
"How do we know that's the law?" asked Breyer. "There are people of good faith on both sides of this argument" who may disagree about the other law's meaning.