“This is rough business,” said Fred Wertheimer, a veteran advocate of tighter campaign regulations. “We’re not dealing with campaign finance laws. We’re dealing with the essence of power in America.”

The case involves “Hillary: The Movie,” a mix of advocacy journalism and political commentary that is a relentlessly negative look at Mrs. Clinton’s character and career. The documentary was made by a conservative advocacy group called Citizens United, which lost a lawsuit against the Federal Election Commission seeking permission to distribute it on a video-on-demand service. The film is available on the Internet and on DVD. The issue was that the McCain-Feingold law bans corporate money being used for electioneering.

A lower court agreed with the F.E.C.’s position, saying that the sole purpose of the documentary was “to inform the electorate that Senator Clinton is unfit for office, that the United States would be a dangerous place in a President Hillary Clinton world and that viewers should vote against her.”

At the first Supreme Court argument in March, a government lawyer, answering a hypothetical question, said the government could also make it a crime to distribute books advocating the election or defeat of political candidates so long as they were paid for by corporations and not their political action committees.

That position seemed to astound several of the more conservative justices, and there were gasps in the courtroom.

“That’s pretty incredible,” said Justice Samuel A. Alito Jr.

The discussion of book banning may have helped prompt the request for re-argument. In addition, some of the broader issues implicated by the case were only glancingly discussed in the first round of briefs, and some justices may have felt reluctant to take a major step without fuller consideration.

The question of what Congress may do to regulate books is a hypothetical one: the relevant law, the Bipartisan Campaign Reform Act of 2002, more commonly called McCain-Feingold, applies only to broadcast, satellite or cable transmissions. That leaves out old technologies, like newspapers and books, and new ones, like the Internet. But the constitutional principles involved, some of the justices suggested, ought to apply regardless of the medium.