Mr. Cruz rails against illegal immigrants; Mr. Rubio takes a more welcoming approach. Mr. Cruz opposed President Barack Obama’s fast-track trade bill; Mr. Rubio supported it. Mr. Cruz traffics in the highflying oratory of an evangelical minister’s son; Mr. Rubio’s brand of eloquence is more low key.

Both senators still trail the political novices— Donald Trump and Ben Carson—who lead the GOP field. But the Cruz-Rubio surge raises a surprising prospect: Two Cuban Americans are moving from long-shot to top-tier candidates in a party that has struggled to win support from Hispanic voters.

Mr. Cruz said in a recent CNN interview it was “plausible” that the primary would wind up being a Rubio-Cruz faceoff, citing a history of GOP contests that pitted a conservative against a more-moderate candidate.

“I think Marco is certainly formidable,” Mr. Cruz said. But, he added, ”once it gets down to a head-to-head contest between a conservative and a moderate…I think the conservative wins.”