Redistricting — the process of drawing new legislative maps every decade — has long been the blood sport of American politics. Supreme Court justices on Tuesday debated just how deeply they want the federal courts to wade into that.

Justices across the political spectrum said partisan gerrymandering is distasteful, but during oral arguments on a case out of Wisconsin, conservative members said they saw little chance of limiting the courts’ role if they start to get involved.

Chief Justice John G. Roberts Jr., who has long been seen to view protecting the majesty of the court as a paramount goal, worried what voters would think if judges strike down state maps by ruling that one party was destined to too many seats.

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“We will have to decide in every case whether the Democrats win or the Republicans win,” the chief justice said. “That is going to cause very serious harm to the status and integrity of the decisions of this court in the eyes of the country.”

Wisconsin state officials acknowledged that they were aiming to help Republicans when the Legislature and governor — all under Republican control — redrew the lines after the 2010 census. They packed Democrats into relatively few districts, where Democratic candidates easily won, then spread Republicans more evenly among districts to benefit their party’s candidates.

That led to a situation in 2012 where Republicans won less than 49 percent of the vote among those who cast ballots for the state Assembly but garnered 60 of the 99 seats.

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Paul M. Smith, the attorney for Democratic voters who challenged Wisconsin’s map, said that if the court didn’t intervene, then every state that leaves redrawing to politicians will follow Wisconsin’s lead and draw districts where the party affiliation of the winner is never seriously in doubt.

“It may be that you can protect the court from seeming political, but the country is going to lose faith in democracy big time because voters everywhere are going to be like the voters in Wisconsin and [say], ‘No, it really doesn’t matter whether I vote,” Mr. Smith told the justices, countering the chief justice’s fear of politicization.

Mr. Smith said legislatures that stand to benefit aren’t going to fix themselves and neither will Congress.

“You are the only institution in the United States that can solve this problem, just as democracy is about to get worse,” he told the court.

Justices have struck down plans over racial gerrymanders and have said in previous rulings that extreme partisan gerrymanders could be illegal. But the court has never struck down a map specifically over partisanship.

Part of the difficulty has been to come up with a credible test.

Voting rights activists say they have one, thanks to the latest social science research that promises to calculate the number of votes “wasted” because voters were packed into districts for partisan reasons.

Other social scientists, though, question whether that screen is solid enough. They say the “efficiency gap” test would invalidate plans written by supposedly neutral judges.

Indeed, Wisconsin’s attorneys said that of the 17 worst maps identified by the efficiency gap method, 10 were drawn by neutral arbiters such as nonpolitical commissions or by federal judges.

Erin E. Murphy, the attorney for the Wisconsin Senate, said those “false positives” proved the “EG” test is fatally flawed.

“At the end of the day, what matters is how people vote in elections,” she said.

Chief Justice Roberts called the calculations “sociological gobbledygook” and repeated his fears of being dragged into a boondoggle.

The law calls for any federal challenges to districts to be heard by a three-judge panel at the district court, with appeals coming directly to the Supreme Court.

“The whole point is you’re taking these issues away from democracy and throwing them into the courts,” the chief justice said.

Court watchers have predicted that the case could come down to a split with Justice Anthony M. Kennedy in the deciding role. In previous cases, he has sought good tests for identifying bad plans.

He didn’t tip his hand on Tuesday, though he did pressure Wisconsin on whether it would be illegal for a state to explicitly call for maximizing political advantage for one party or another as part of its redistricting process.

After some prodding, the attorney for the state Senate said she believed that would cross a line.

Justice Stephen G. Breyer offered a multipart test that he said could cut through the clutter. He said if a single party controlled the process, if the map led to a major disparity between percentage of votes and the end result of seats and if it was deemed to be persistent across elections, then it could be questioned.

“I suspect that’s manageable,” he said.

Justice Sonia Sotomayor said that in Wisconsin’s case, Republican legislators kept sending the map back to squeeze out more partisan advantage. She said if challengers could prove the state sought the most partisan map possible, that should be enough.

It’s possible the justices never get to the merits of the case. Some members of the court, including Justice Kennedy, questioned whether the lead plaintiff challenging Wisconsin’s map could bring the case because he lived outside the districts in question.

He argued that he had standing to sue because the state’s maps affect the makeup of the Legislature. But several justices suggested that his claim would have been stronger if he was affected by the redrawing.

Outside the court building, former California Gov. Arnold Schwarzenegger led a rally on the case, telling the crowd that “it’s time to terminate gerrymandering.”

Mr. Schwarzenegger, who as governor pushed California to move redistricting from politicians’ hands to a citizen commission, said high re-election rates are proof that the system is “fixed” and Congress won’t change it.

“Herpes and colonoscopies are more popular than Congress, but for some miracle reason, 98 percent of them get re-elected,” he said. “It’s a system where the politicians are picking the voters, rather than the voters picking the politicians.”

⦁ Alex Swoyer contributed to this report.