Mr. Cruz, for one, said his Texas support has been uplifting. “The many supportive letters, e-mails, calls and social media comments we’ve received from Texans since Labor Day have been inspirational,” he said in a statement. “Hearing from constituents keeps me focused on the concerns of the people I work for and the issues I ran on. That’s what matters.”

Of course, not everyone is applauding, particularly Democrats in Texas, where Republicans control both houses of the Legislature.

“I just kind of shake my head and say, ‘I don’t believe this guy is for real,’ ” said State Senator John Whitmire, a Houston Democrat. “Many individuals in his own party say he has helped the Democrats. I’m more concerned about what he’s done to the country than the good he’s done to any Democratic effort.”

Moderate and establishment Republicans in Texas privately grumble about Mr. Cruz and his handling of the budget fight. They criticize the wisdom of forcing a government shutdown over a health care law that the Supreme Court validated, and wondered how much of Mr. Cruz’s battle was done to benefit his presidential aspirations.

“I grit my teeth and bear it,” said a prominent Texas Republican, who spoke on the condition of anonymity because he said he wanted to avoid an intraparty fight. “I really hope he implodes sooner rather than later.”

One of the few public displays of any Texas backlash came in an editorial on Wednesday in The Houston Chronicle. Headlined “Missing Kay,” the editorial criticized Mr. Cruz, whom the paper endorsed last year, for being “part of the problem in specific situations where Hutchison would have been part of the solution.” But even that criticism was muted. When news outlets reported that The Chronicle had “unendorsed” Mr. Cruz, the paper’s editors clarified that they did not pull their endorsement, but were evaluating the work of elected officials in an “active, ongoing process.”

The doubts from Texas Republicans invariably play out behind closed doors. They do not fear Mr. Cruz’s personal wrath, but that of his supporters and the possibility of a primary fight if they criticize him. Mr. Cruz won his Senate seat by defeating one of the most powerful Republicans in Texas, Lt. Gov. David Dewhurst, a victory that exposed the ideological split between moderate establishment Republicans and the younger, more aggressive and conservative movement of grass-roots activists and Tea Party supporters.