Some Democrats may nevertheless approach the issue with caution.

Mary Burke, who is expected to win the Democratic nomination to challenge Wisconsin's Walker, said she supports legislation there to increase the minimum wage by a relatively modest 35 cents an hour to $7.60.

Beyond that, the former state commerce secretary and daughter of Trek Bicycle's founder said a gradual and fair increase in the minimum wage could avoid economic harm. While she wasn't prepared to say what that is, the subject will be prominent in her campaign, Burke said.

"This race is going to be about jobs and people being able to support themselves," Burke said, "and that is an important way we can help more people move toward economic independence."