Alito took the bench Tuesday, and the very first case that justices agreed to hear was on the contentious issue.
Justices announcedon what opponents call partial-birth abortion. The ruling next year will coincide with the startup of presidential campaigns.
Alito could well be the tie-breaking vote when the court decides if doctors can be barred from performing the abortion procedure. He succeeded Justice Sandra Day O'Connor, a moderate abortion-rights supporter.
"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."
As a young government lawyer, Alito stated in a job application that he was "particularly proud" of his work on cases arguing that the Constitution does not protect the right to an abortion. He also counseled other lawyers in the Justice Department in 1985 to gradually chip away at abortion rights rather than try to immediately overturn the landmark 1973 Roe v. Wade ruling.
The Bush administration had sought the Supreme Court's intervention, and conservatives cheered the announcement.
"This is the frontline abortion case in the country," said Jay Sekulow, chief counsel for the American Center for Law and Justice, which represents members of Congress in the case.
Even with O'Connor's retirement, there are five votes to uphold Roe. What is likely to happen, reports CBS News legal analyst Jan Crawford Greenburg, is that states will have greater leeway "to step in and regulate abortion, to say this kind of procedure is OK, this kind of procedure is not. That's what this new court is most likely to do in the years to come."
Crawford Greenburg adds that more power with the states is "something the Supreme Court has not previously allowed with Justice O'Connor on the court."
Abortion rights groups are worried that the new court might make it easier for legislators to limit women's access to abortions.
"The stakes in this case are not whether Roe v. Wade will be overturned, but whether a major pillar of Roe v. Wade will be reconsidered," said Nancy Northup, president of the Center for Reproductive Rights, which represents doctors who have contested the law.
Congress voted in 2003 to prohibit the type of abortion, generally carried out in the second or third trimester, in which a fetus is partially removed from the womb and its skull punctured or crushed.
Justices were told that 31 states had barred such abortions over the past eight years.
The Supreme Court split 5-4 in 2000 in striking down a state law barring the same procedure because it lacked an exception to protect the health of the mother. O'Connor, the tie-breaking vote, retired late last month and was replaced by Alito.
Doctors who perform the procedure contend it is the safest method of abortion when the mother's health is threatened by heart disease, high blood pressure or cancer.
It's not clear how often the procedure is done, but nearly nine in 10 abortions are performed in the first three months, according to government estimates.
The 2003 law was passed following nearly a decade of attempts by Republican leaders and two vetoes by former President Bill Clinton.
"It was clear in 2003 when it said that you could not limit this procedure unless certain exceptions were in place," Cohen says. "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."
The law was never put in effect. It was struck down by judges in California, Nebraska and New York, again because it had no exception to protect the women's health.
Defenders of the law maintain that the procedure is never medically necessary to protect a woman's health.
The Supreme Court recently dealt with an abortion case from New Hampshire. Justices on a 9-0 vote 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.
Fifteen states urged justices to review the latest case: Alabama, Arkansas, Colorado, Florida, Idaho, Kansas, Michigan, Missouri, Ohio, Pennsylvania, South Carolina, South Dakota, Texas, Utah and Virginia.
The case is Gonzales v. Carhart, 05-380.