But he was picky: Cornyn didn't even get the support of his fellow Texas senator, though he still routed Congressman Steve Stockman, who ran a bizarre campaign.
"I say they are not going far right enough," said Marlin Robinson, 56, after casting his primary ballot in Houston. "They need to go farther right as far as I'm concerned because I'm tired of this liberal crap that's running this country."
With Abbott and Davis advancing to the November ballot, the showdown is poised to become a record-shattering arm's race of fundraising in a Texas gubernatorial election.
Democrats set on breaking the nation's longest losing streak in races for statewide office, meanwhile, hoped a charismatic headliner in Davis would turn out long-dormant voters.
Her underdog campaign has raised $16 million so far behind a whopping 91,000 individual donors and big checks from abortion-rights groups.
"If people don't start supporting the Democratic Party and voting as a Democrat, instead of being a Democrat voting in the Republican primary, then we're never going to win races and we're never going to establish ourselves as a serious party here," said Janet Veal, 43, a student adviser at Texas Tech University who cast a ballot in Lubbock on Tuesday.
Some Texas GOP candidates pledged to further tighten some of the nation's strictest abortion laws and double down on the state's gay marriage ban — one of several state bans recently ruled unconstitutional by federal courts.
"I think we need to bolster the border security and get tougher on immigration," 38-year-old conservative Republican Glendon Paulk said after voting in Lubbock. "I'm all for people who come over here legally but the illegal immigrants, it doesn't make sense for them to get a break while we're working and having to pay taxes."
Frigid weather greeted some voters with a dangerous drive to the polls. Austin locations opened late because of icy conditions and extended voting for two hours. Turnout was light in many places, with election workers seen knitting or reading a newspaper in between voters' sporadic arrivals.
The last time Texas had so many open statewide seats was 2002, when Perry won his first full term. While Democrats ran mostly unopposed in their primaries, crowded fields in the Republican races also ended in runoffs for attorney general and agriculture commissioner.
Illinois holds the nation's next primary March 18, followed by a flood of state primaries in May and June.
Associated Press writers Will Weissert and Chris Tomlinson in Austin, Juan Carlos Llorca in El Paso, Betsy Blaney in Lubbock, and Ramit Plushnick-Masti and Michael Graczyk in Houston contributed to this report.
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