Republican Party officials and activists in Midwestern states say a GOP candidate can reverse President Barack Obama’s 2008 victories in the region. But they’re still trying to determine who has the best shot.

Mitt Romney, a Michigan native and son of a former Michigan governor, has a home-field advantage and a feel for Midwestern political culture that some party officials say they prefer. Others say job losses in the region leave an opening for Rick Perry, the Texas governor and Mr. Romney’s top opponent, who is campaigning on the basis of strong jobs growth in his state.

At the same time, some Republicans expressed misgivings about Mr. Perry’s durability after his shaky performance in a GOP debate last week in Orlando, Fla.—