OXFORD, Ohio – Facing what is emerging as a defining issue, Mitt Romney running mate Paul Ryan on Wednesday invited debate over his controversial proposal to overhaul Medicare and predicted the GOP would win the argument.

“We want this debate. We need this debate. And we will win this debate,” Ryan told supporters on the campus of his alma mater, Ohio’s Miami University.

Romney named Ryan, a seven-term Wisconsin congressman, as his running mate on Saturday. Since then, Democrats have pounced on the plan he authored as House Budget Committee chairman to transform the popular health-care system for seniors.

Over the past week, however, Ryan did not directly address the intensifying criticism — or even simply say the word “Medicare” during multiple campaign stops across six states. He addressed the issue in a handful of media interviews, but he avoided it while facing voters.

That changed Wednesday, the same day President Obama weighed in as well.

Obama told an Iowa audience that he strengthened Medicare, despite charges from the Romney campaign that the president actually weakened the law by cutting more than $716 billion from the program as part of his health care overhaul.

But Ryan said that Obama had “raided” the program. It was the same charge that Romney had levied earlier in the day during a campaign stop in North Carolina.

Neither man mentioned that Ryan’s congressional budget proposal includes the same savings, which are supposed to be realized through lower medical payments and great efficiencies in the program.

In an election expected to hinge on the nation’s struggling economy, Ryan’s selection has thrust Medicare into the forefront of the debate. The program serves tens of millions of seniors. The issue may be particularly significant in swing states that have large elderly populations, Florida, Iowa and Pennsylvania among them.

The Romney campaign argues that major changes are needed to save the program for future generations, while Obama charged Wednesday that the Republican plan “ends Medicare as we know it.”

Ryan also echoed Romney’s sentiment that the president’s re-election effort “is all about division and attack and hatred.”

In Ohio for a two-day campaign swing, Ryan told the Miami University audience that Obama is running a campaign “based on anger and division.”