Ohio Gov. John Kasich said he isn't willing to serve as anyone's vice president, but he indicated party affiliation would not matter to him when choosing his own running mate.

After losing the Arizona primary and trailing a candidate who is no longer running for president, Kasich hit the campaign trail in Wisconsin and told voters only he could beat the Democrats in November.

He ruled out the possibility of serving with any GOP nominee, but would not oppose putting a Democrat near the top of the Republican ticket himself in November.

"I'm going to be nobody's vice president, OK?" Kasich said, interrupting a questioner at a town hall in Wauwatosa. "I will not be anybody's vice president. Just so you know."

The questioner then asked whether the Ohio governor would consider selecting a Democrat as his vice presidential running mate. Kasich avoided immediately answering the question before indicating he would not rule out working with a Democrat.

"If you're going to bring somebody over they need to know what you're about. And they can't spend their time trying to pick at you and undermine you because, frankly, we don't have enough time to do it," Kasich said. "Just because someone happens to be a Democrat doesn't mean they're disqualified. President Obama, he had his secretary of defense, Bob Gates, a Republican. And I think Bob did a fantastic job for him."

Kasich asked Wisconsinites to unite behind his campaign and learn more about him before the April 5 primary. For those who want to know more about how he "labored in obscurity" in Ohio, Kasich suggested they ask their own governor, Scott Walker, who Kasich said has done the same in Wisconsin.