But the case before the court could have a profound effect as well on what adults are allowed to access online.
A lower court has ordered the government not to implement the Child Online Protection Act, saying it unconstitutionally relies on community standards to define harm to children.
The battle over pornography on the Internet extends well beyond the boundaries of the current case.
The lines between the federal government and such organizations as the American Civil Liberties Union were first drawn over the 1996 Communications Decency Act.
The act prohibited the "knowing" transmission of "indecent" messages over the Internet to anyone younger than 18.
The ACLU and others challenged the law in court. Eventually, the Supreme Court said the government had a "compelling interest" in protecting minors from "indecent" material online -- material that was less offensive than obscenity -- but ruled that the act was not the least restrictive way to accomplish that goal, and struck it down as unconstitutional.
When the Communications Decency Act crashed and burned, Congress enacted the Child Online Protection Act, or COPA, to replace it, and President Bill Clinton signed the act into law in 1998.
COPA includes civil and criminal penalties for anyone who "knowingly ... by means of the World Wide Web, makes any communication for commercial purposes that is available to any minor and that includes any material that is harmful to minors."
It defines those materials as those in which "the average person, applying contemporary community standards," would find three things.
No. 1, that the material "is designed to appeal to, or is designed to pander to, the prurient interest;" No. 2, contains some sexual element and, No. 3, "lacks serious literary, artistic, political or scientific value for minors."
The law said an "affirmative defense" to prosecution would be a "good faith" attempt to keep the material from minors.
However, an ACLU-led coalition again challenged the law, and a federal judge issued a preliminary injunction against its implementation. Eventually, a federal appeals court in Philadelphia agreed with the judge, saying COPA was probably unconstitutional.
The appeals court said COPA's reliance on community standards "in and of itself, imposes an impermissible burden on constitutionally protected First Amendment speech." The community standards threshold "as applied to the Internet means than any communication available to a nationwide audience will be judged by the standards of the community mostly likely to be offended by the message," the court said.
Use of a "community standard" meant that Web publishers would need to either severely censor themselves or establish some kind of age or credit card verification for material that "might be deemed harmful by the most puritan of communities in any state," the appeals court said.
The Bush administration then asked the Supreme Court to take the case and settle the community standards issue.
Speaking to the justices during argument Wednesday, U.S. Solicitor General Theodore Olson repeatedly stressed that government, apart from parents, has its own interest in protecting children.
"All three branches of our national government have determined that pornography causes incalculable and substantial damage to our children," Olson said.
Compounding the problem, pornography is readily available on the Internet, he argued.
"COPA is Congress's answer to that problem," Olson told the justices.
He said the 1997 decision by the Supreme Court on the Communications Decency Act "explains how to solve pornography in a constitutional manner," and COPA was constructed with that decision in mind.
Olson agreed with Justices Anthony Kennedy and Stephen Breyer that the high court could throw out the lower-court ruling, but said that "community standards" should be interpreted as "national standards."
That would prevent a jury from applying the standards of the most prudish community to material that can legally be seen by adults, Olson said.
However, he added, jurors would still have to use their own experience in deciding what that national standard is.
And it would still be constitutional "for juries in different parts of the country to reach different conclusions about the same material."
Olson said Internet pornography was an $8 billion a year business operated from 28,000 sites on the World Wide Web.
"This is readily accessible to children," he argued. "As long as they can type and read, they will find it. They will find it by accident."
Speaking for the ACLU coalition that challenged the law, New York attorney Ann Beeson put the case in a different light.
"COPA ... makes it a crime to communicate (constitutionally) protected speech to adults on the Internet," she told the justices.
"Most communities feel providing information" about sex to children "is sinful," she added.
One of her clients, Beeson said, the Sexual Health Network, teaches the disabled how to continue a relatively sexual life.
Such sites are principally what "the government wants to prosecute," she contended.
Breyer repeatedly reminded Beeson from the bench that the Supreme Court had taken the case only to resolve the "community standard" issue.
But Beeson responded that even if juries are instructed to apply a national standard, the law would still be unconstitutional -- "The least tolerant community gets to set the standards for the 'Net.'"
The most effective way to protect children from porn on the Internet, she said, is for parents to install filters that prevent children from accessing sexual sites.
The Internet is an ever-changing venue for the exchange of ideas, Beeson argued. "COPA threatens to transform this dynamic medium into one only fit for children."
The Supreme Court should hand down a decision in the case sometime this winter or early spring.
(No. 00-1293, Ashcroft vs. ACLU et al)