But when Mr. Cruz went to New York City to meet with donors this summer, he privately offered a different view of Mr. Paul: The Kentucky senator can never be elected president, he told them, because he can never fully detach himself from the strident libertarianism of his father, former Representative Ron Paul of Texas.

Word of Mr. Cruz’s remarks reached Mr. Paul’s inner circle, touching off anger and resentment…

Mr. Paul’s inner circle privately derides Mr. Cruz as “the chief of the wacko birds,” echoing a phrase from Senator John McCain of Arizona. And, while allowing Mr. Cruz to lead the charge on Obamacare, the Kentucky senator has quietly been reaching out to more establishment forces within the Republican Party, trying to prove to big donors and mainline Republican organizations that he is more than a Tea Party figure or a rerun of his father’s failed candidacies…

“Both of them are appealing to the same base, but there is no doubt that Cruz is the one who now has got a full head of steam,” said Bob Vander Plaats, who leads an Iowa Christian conservative group.

Supporters of Mr. Paul are better organized, however, and building on Ron Paul’s campaign, they have essentially taken over the levers of the Iowa Republican Party, earning the nickname “Paulistinians” in the state’s Republican circles. They tend to be libertarian-leaning and as passionate about limiting American interventionism overseas as they are about domestic affairs.