Senator Ted Cruz has long cheered Donald J. Trump’s presence in the Republican presidential field, thanking him for focusing national attention on issues like border security.

Speaking to donors in New York City on Wednesday, Mr. Cruz suggested a more strategic reason to be grateful: Mr. Trump is bending the race in Mr. Cruz’s direction.

“He has framed the central narrative of this primary as, ‘Who will stand up to Washington?’ ” Mr. Cruz, of Texas, said at the private fund-raiser, echoing remarks he has made publicly. “Now if that’s the central narrative, the natural next question is, ‘O.K., who has stood up to Washington?’ ”

Mr. Trump, in this view, has taken a machete through the brush for Mr. Cruz, allowing him to rise quietly despite his own reputation for bombast, while Mr. Trump absorbs the scrutiny a front-runner attracts and eventually peters out, as Mr. Cruz has wagered.