One senator used the word “wariness.” Another said that an unpersuasive argument for getting one on board with legislation would be pointing out that it was championed by the other. They, like other senators and staff members, spoke on the condition of anonymity to speak frankly about their colleagues.

Now both 44 and eager to become the first Latino president, Mr. Rubio and Mr. Cruz are content to stay out of each other’s way on the campaign trial, both seeming more concerned now with clearing out competitors in their respective lanes. It was no accident that Mr. Rubio sparred in the debate with Jeb Bush, his rival for the support of Republican establishment donors. Or that Mr. Cruz steered clear of any conflict as he spoke directly to the camera about his born-again father in an effort to solidify his support among evangelicals.

But they are already competing in the Senate for the endorsement of Senator Mike Lee of Utah, who is admired by the conservative base for his anti-spending positions, and whose backing is considered a conservative seal of approval.

Mr. Cruz has made an overt pitch to Mr. Lee, talking about his success in fund-raising, why he stacks up better against the other candidates and why different pools of conservative voters will coalesce around him when, in his telling, the campaigns of Donald J. Trump and Ben Carson inevitably evaporate, according to a person with knowledge of the conversations.

But a recent spat in a Senate Judiciary Committee hearing exposed signs of strain in the relationship between Mr. Cruz and Mr. Lee, who in the past had been described, to the annoyance of Mr. Lee, as Batman and Robin. In the hearing, Mr. Cruz argued that measures proposed by Mr. Lee would weaken punishment of violent offenders, which Mr. Lee called a mischaracterization.

Mr. Rubio seems ready to capitalize, though in a subtle manner more reflective of his congenial style. He has made a point of asking Mr. Lee about his family, said a person with knowledge of those conversations. And Mr. Rubio’s “super PAC” airs ads in New Hampshire championing a tax plan he and Mr. Lee sponsored.

The two candidates declined to comment about their relationship, but their advisers sought in interviews to tamp down any notion of tension, while acknowledging their differences. On a more personal level, Mr. Cruz’s musical tastes are country, while Mr. Rubio’s run toward West Coast rap, and they have shared few, if any, meals outside the Senate. Nevertheless, the advisers described a collegial relationship based on common backgrounds — both talk of their Cuban émigré families on the campaign trail, and oppose President Obama’s opening of ties to Cuba — and an ability to rib each other over political headaches (the government shutdown for Mr. Cruz, immigration policy for Mr. Rubio).