In Winterset, Iowa, Monday night, attendees at a Ted Cruz town hall sat through a 10-minute video of Ron Paul 2012 supporters talking about how they’re now backing the Texas senator’s presidential campaign.

It’s part of Mr. Cruz’s effort, having consolidated support from the state’s social conservatives, also to win over libertarian-minded supporters from Mr. Paul, who placed second in Iowa’s presidential caucuses in 2008 and third in 2012.

Ron Paul’s son has something to say about that.

“I don’t think that Ron Paul supporters are very excited about making the sand glow in the Middle East,” Kentucky Sen. Rand Paul said, referring to Mr. Cruz’s oft-repeated declaration of what he would do to combat Islamic State militants.

In a Wall Street Journal interview Friday while he was riding from Des Moines to Oskaloosa, the younger Mr. Paul, who is running for president this year, said Mr. Cruz will lose support from people who backed his father for his claims that he expanded the government’s surveillance capabilities in the Freedom Act that passed last year.