Compounding the problem is Mr. Cruz himself. He often portrays this election as akin to 1980, when Ronald Reagan won in a landslide. But he appears to be privately grappling with whether he would be better off playing the 1976 version of Reagan, who carried the banner of unadulterated conservatism against the eventual Republican nominee all the way to the convention, fell short and won four years later.

Though Mr. Cruz has adjusted his public tone, calling for party harmony and appealing to “our better angels” in a moment of political discord, senior Republican officials say Mr. Cruz has made little effort to repair relationships, particularly in the Senate.

Senator John Cornyn, the second-ranking Republican senator and Mr. Cruz’s fellow Texan, privately lobbied Mr. Cruz to attend a Senate Republican luncheon in the Capitol and soothe feelings, according to a Republican strategist briefed on the request. But after a CNN report in which some Republican senators suggested that Mr. Cruz apologize to the Senate majority leader, Mitch McConnell, whom Mr. Cruz called a liar on the Senate floor, Mr. Cruz’s campaign became irritated and backed off a peacemaking lunch.

Mr. Cruz and Mr. McConnell have still not spoken, according to an aide to Mr. McConnell.

“I’m not sure there’s anything to apologize for,” Jason Johnson, Mr. Cruz’s chief strategist, told reporters recently.