The Supreme Court has never struck down a voting map on the grounds that it was drawn to amplify the power of the political party in control of the state legislature. But Justice Kennedy, in his questions last term and in a 2004 concurring opinion, left the door open to the possibility that some kinds of political gamesmanship may be too extreme.

In their Supreme Court brief, North Carolina lawmakers asked the court to close that door. The Constitution, they wrote, contemplated a role for politics in redistricting by assigning the task to state legislatures, adding that federal courts have no role to play in supervising the legislatures’ judgments.

“The time has come,” they wrote, “for this court to make clear that the Constitution does not provide courts with the tools or the responsibility to say how much partisan motivation is too much.”

The lawmakers warned the Supreme Court that its authority would be threatened if it were seen to be making political choices. That was an echo of comments from Chief Justice John G. Roberts Jr. in the argument in the Wisconsin case.

“We will have to decide in every case whether the Democrats win or the Republicans win,” he said, adding, “And 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.”

Partisan gerrymandering is almost as old as the nation, and both parties have used it. Indeed, in a companion case from Maryland that will be argued the same day as the one from North Carolina, Republican voters are challenging a district drawn by Democratic lawmakers.

But in recent years, as Republicans captured state legislatures around the country, they have been the primary architects and beneficiaries of partisan gerrymandering. Using increasingly sophisticated software, they have drawn voting districts to favor their party’s candidates.