AMES, Iowa—Iowans this past weekend had their pick of corn dogs, pork chops, Rick Santorum or Ted Cruz.

The first two offerings were popular delicacies at the state fair. The others are Republicans already jockeying over what is expected to be a wide-open 2016 presidential race, barely nine months after the latest one concluded and more than two years before any party primaries would start.

Mr....