Wisconsin’s judiciary, officially nonpartisan, has been marred in recent years by political intrigue, divisive elections and even accusations of one judge placing another in a chokehold.

Now it may decide the fate of the outgoing governor’s new laws to limit the power of his successor.

“There will be a challenge, no doubt,” Gov. Scott Walker said a few days before he signed bills expanding the power of legislative Republicans he teamed up with over the last decade. “They’ve challenged just about everything we or lawmakers have done.”

The threat of litigation has rarely dissuaded Mr. Walker, a Republican who reshaped Wisconsin in his conservative image and who signed the power-shifting measures on Friday afternoon as one of his final acts in office. The judiciary has upheld several of Mr. Walker’s signature policies in recent years, despite challenges from the left. And as Mr. Walker predicted, liberal groups quickly vowed legal action on the new legislation.

“This is a shameful attack on our democracy by politicians who will do anything to hold onto power,” said Eric H. Holder Jr., an attorney general under President Barack Obama who leads one of the groups that has promised a court fight. In a statement, Mr. Holder called the new laws “grossly partisan” and “deeply undemocratic.”