Updated at 6:35 p.m., with more from Cruz, who told reporters Friday that he does not plan to get involved in any primaries featuring incumbents. 

Sen. Ted Cruz (R-Tex.) has attracted widespread attention during his first few months on Capitol Hill for many reasons. His role as vice chairman of the National Republican Senatorial Committee isn't one of them.

(Mike Fuentes/Bloomberg) (Mike Fuentes/Bloomberg)

Cruz has been quiet publicly about what, if anything, he's been doing behind the scenes for the committee. And in an interview earlier this month, he shed little new light on the matter. But he did make a couple of things clear: The committee shouldn't meddle in primaries, but he very well might.

"In my view, primary elections should be determined by the voters of each state. So I don’t think the National Republican Senatorial Committee should be involved in primaries,” Cruz said in the interview.

He later added, "I hope and expect personally to get involved in some races and indeed in some primaries, but to date have not done so yet."

Cruz offered more clarity about his strategy here in New Hampshire on Friday, telling reporters he intends to "stay out" of primaries involving incumbents, including the bid of fellow Texas Republican Sen. John Cornyn, the second-ranking Republican in the Senate.

“I think it is likely that I am gong to stay out of incumbent primaries across the country, either supporting incumbents or opposing incumbents,” Cruz said.

Cruz insisted in the interview this month that if he does involve himself in a Republican primary, it would be in his own individual capacity as a senator, not on behalf of the committee.

Even so, Cruz's position as vice chair means he is not just another senator. And getting involved on his own could complicate the picture, prompting questions about where the Senate Republicans' campaign arm stands. In addition, the fact that he is unwilling to back his colleagues for reelection could stoke tension in his relationships with them.

"Senator Cruz has been a great asset and tireless advocate of the NRSC," said NRSC spokeswoman Brook Hougesen earlier this week when asked about Cruz's remarks in the interview.

When Cruz was tapped last fall as one of two vice chairs (Sen. Rob Portman (R-Ohio) is the other) under Chairman Jerry Moran (R-Kan.), it was seen as a signal he could be willing to play ball with the GOP establishment. It was also seen as an opportunity for the NRSC to build inroads with the conservative groups and activists with whom they have sometimes locked horns, because those groups and activists adore Cruz.

It's still possible that Cruz might do those things. But so far, there are no signs that his presence has fundamentally changed anything for the committee. And if anything, the early signals suggest the relationship could be complex.