If she's a "social-values" Republican, that might be an issue.
If she's truly a "small government" Republican, you might be okay. Just be warned that many of the people that claim to want the government out of people's lives really mean, "We want the government out of businesses lives so they can do what they want, but they absolutely should be in the bedroom to make sure nobody has any type of sex I don't like."
I've met both types of Republicans, and disagree with both, but I can live with and enjoy the company of the group of Republicans that isn't trying to enforce their moral values upon my life. It's hard to enjoy the company of someone who wants the government to enforce some set of morals on me, though, so the other type isn't as fun to be around.