"I'm proud to be a Republican, but I believe my policies appeal to many Democrats," he said during an appearance in Vienna, Ohio, outside Youngstown.
"If you're a Democrat and you want America to be strong and confident in our ideals, I would be honored to have your vote."
Bush, sharing the stage with maverick Democratic Sen. Zell Miller, hammered rival John Kerry for his votes on Iraq, views on terrorism and votes against partial-birth abortion, contrasting Kerry's values with those of past Democrats -- from Franklin D. Roosevelt and Harry Truman to Lyndon Johnson and Daniel Patrick Moynihan.
"I know that Democrats are not going to agree with me on every issue, yet on the big issues of our country's security, victory in the war against terror, improving our public schools, respecting marriage and human life, I hope people who usually vote for the other party will take a close look. ...If you are a Democrat and your dreams and goals are not found on the far left wing of the Democratic Party, I'd be honored to have your vote.