The Bush administration has pressed the high court to reinstate the federal law, passed in 2003 but never put in effect because it was struck down by judges in California, Nebraska and New York.
The outcome will likely rest with the two men that President Bush has recently installed on the court. Justices had been split 5-4 in 2000 in striking down a state law, barring what critics call partial birth abortion because it lacked an exception to protect the health of the mother.
But Justice Sandra Day O'Connor, who was the tie-breaking vote, retired late last month and was replaced by Samuel Alito. Abortion had been a major focus in the fight over Alito's nomination because justices serve for life and he will surely help shape the court on abortion and other issues for the next generation.
"This will be a case where the switch from Justice O'Connor to Justice Alito makes all the difference in the world," says CBS News legal analyst Andrew Cohen. "She ruled against the effort to ban this procedure a few years ago but he has given the clear sense that he would be much more receptive to the restrictions in play here.
The federal Partial-Birth Abortion Ban Act prohibits a certain type of abortion, generally carried out in the second or third trimester, in which a fetus is partially removed from the womb, and the skull is punctured or crushed.
Justices on a 9-0 vote in a New Hampshire case reaffirmed in January that states can require parental involvement in abortion decisions and that state restrictions must have an exception to protect the mother's health.
The federal law in the current case has no health exception, but defenders maintain that the procedure is never medically necessary to protect a woman's health.
Even with O'Connor's retirement, there are five votes to uphold Roe, the landmark ruling that established a woman's right to an abortion.
Alito's views "are not going to change the outcome of the central principle of Roe v. Wade," said John Garvey, the dean at Boston College Law School. "In some ways, these are tokens or markers in ... a symbolic tug of war."
Mr. Bush has called the so-called partial birth abortion an "abhorrent practice," and his Supreme Court lawyer, Solicitor General Paul Clement, had urged justices not to delay taking up the administration's appeal.
The case that will be heard this fall comes to the Supreme Court from Nebraska, where the federal law was challenged on behalf of physicians. Doctors who perform the procedure contend that it is the safest method of abortion when the mother's health is threatened by heart disease, high blood pressure or cancer.
"The court almost had to take up this issue again," said Cohen. "It was clear in 2003 when it said that you could not limit this procedure unless certain exceptions were in place. Congress then enacted a law without those restrictions and now the court will have to decide whether the justification for the Congressional action is constitutional or not. It should be a very close case, almost certainly a five-four ruling."