Mr. Cruz’s victory has inspired other Texas Republicans to veer sharply right and to disregard the notion that they have to wait their turn for higher office. Mr. Delisi called it “the Cruz effect.”

“Texas politics has been defined by very careful, plodding and patient down-ballot officeholders,” said Mr. Delisi, a consultant to State Representative Dan Branch, a Republican who is running for attorney general. “Ted Cruz completely turned that on its ear. You can have a lawyer in his 40s upset the food chain and jump to a United States Senate seat.”

Nationally, the main focus on Texas has been the governor’s race, in which Attorney General Greg Abbott seems certain to face State Senator Wendy Davis as his Democratic opponent. But in Texas, most of the attention has been on the Republican primaries.

Candidates for state offices and the seat held by Texas’ senior senator, John Cornyn, who is being challenged by seven fellow Republicans, have appealed to the grass-roots conservatives and Tea Party activists who make up the bulk of the Republican primary electorate. Those appeals have steered the party from the center with tough talk of guns and God and of cracking down on abortion, illegal immigration, same-sex marriage and the Obama administration.

Image George P. Bush is running for land commissioner. Credit Michael Stravato for The New York Times

The decision by Mr. Abbott to campaign with the rock musician Ted Nugent, who had earlier called Mr. Obama a “subhuman mongrel,” was seen by some as one of the dangers to mainstream Republicans of catering to the far right. Mr. Nugent reluctantly apologized for the words, but no Republicans suggested that he was an unacceptable face for the party.

One of Mr. Cornyn’s Republican rivals, Chris Mapp, told The Dallas Morning News that South Texas ranchers should be allowed to shoot anyone who illegally crossed the border onto their property, and he referred to illegal immigrants as “wetbacks.” Mr. Mapp, a businessman from the Gulf Coast town of Port O’Connor, told The San Antonio Express-News that uttering “wetbacks” was as “normal as breathing air in South Texas.” He later said the papers had distorted his comments and took to his Facebook page to say that although he was not politically correct, the country needed “straight talk, and I think we have not had any for a long time.”

Mr. Cornyn’s main challenger — Representative Steve Stockman, a Texas firebrand — has been selling bags that he calls “the official Obama barf bag” for $10 each to raise money for his campaign. Mr. Stockman has made few public appearances and granted few interviews in what has become a bizarre campaign. “It’s a little bit like an Andy Kaufman prank,” Evan Smith, the editor in chief of The Texas Tribune, said on MSNBC, referring to the performance artist from the 1970s and 1980s.