“I’m just holding off until I see what the field looks like,” said Daniel Coats (R-Ind.).

“I’m going to support the nominee of the party,” said Richard C. Shelby (R-Ala.).

“I just hope he spends a lot of time in Iowa, how’s that?” said Joni Ernst (R-Iowa).

The guarded response from Republicans in the Senate, where Cruz has served just over two years, reflects the presidential ambitions of other senators — Lindsey O. Graham (R-S.C.), Rand Paul (R-Ky.) and Marco Rubio (R-Fla.) have openly pondered runs — but also Cruz’s famously sharp-elbowed relationship with his colleagues and the institution he inhabits.