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Texas Sen. Wendy Davis, D-Fort Worth, left, gives a high-five to Sam Peters, 12, after she spoke to supporters at her campaign headquarters Tuesday, March 4, 2014, in Fort Worth, Texas. Davis won the Democratic primary to run for Texas governor.
AUSTIN, Texas—The first primary in what Republicans hope is a triumphant election year sent a message that U.S. Sen Ted Cruz and the tea party still wield considerable influence in one of the nation's most conservative states.

But to find out exactly how much, Texans will have to wait.

In a primary where an extraordinary number of statewide positions were up for grabs following Gov. Rick Perry's decision not to seek another term, some incumbent candidates successfully fought to beat back tea party challengers Tuesday. But several candidates who forced runoffs in May were either praised by the outspoken freshman senator, Cruz, or ran with his no-compromising swagger.

"In Texas, we will show the rest of the country what it means to be conservative," said GOP state Sen. Dan Patrick, who forced longtime Lt. Gov. David Dewhurst into a runoff, less than two years after Cruz beat Dewhurst in the Senate primary.

The primary was the first since Cruz barreled into the U.S. Senate in 2012 and yanked Republicans nationwide further right, and many watched results within Texas to see how strong his influence would be on the state's next generation of Republican leaders. Amid the Republican contests, however, is Wendy Davis, a rising star who has energized the state's Democratic base and is running for governor in November.

Davis, who catapulted to national political stardom last summer with a nearly 13-hour filibuster over abortion restrictions, vowed to topple two decades of GOP dominance in Texas. Though an underdog, she is the first female gubernatorial nominee in Texas since Ann Richards in 1994.

"I will be for all freedoms. Not just certain freedoms for certain people," Davis told supporters Tuesday night after formally securing the nomination, needling Republicans.

With Perry leaving the governor's mansion after 14 years, albeit mulling a second presidential run, Attorney General Greg Abbott coasted to the GOP nomination for the state's top job.

Warnings about Davis' star-making run for Texas governor dealt complacent conservatives a new reason to vote. So did a rare opportunity to select an entirely new stable of leaders.

Abbott, who only three weeks ago unapologetically campaigned with shock rocker Ted Nugent, never mentioned Davis in becoming the GOP's first new gubernatorial nominee other than Perry since George W. Bush in 1998.

"If you're looking for a way to get ahead, if you're looking for a way to succeed or elevate or advance yourself, then I'm your candidate," Abbott said.

Perry's decision to not seek re-election launched a stampede of 26 Republican candidates vying for six of Texas' top offices. Among them was George P. Bush, the 37-year-old nephew of former President George W. Bush and son of former Florida Gov. Jeb Bush, who easily won the nomination for land commissioner in his political debut.

Not all tea party upstarts prevailed: U.S. Sen. John Cornyn and U.S. Rep. Pete Sessions, two of the most powerful Texans in Washington, clobbered their longshot challengers. But others knocked out or were seriously threatening establishment Republicans in the statehouse, which in the past few years has already passed some of the most restrictive voter ID and abortion laws in the country.

Some candidates even started to mimic Cruz's unreserved style.

For Patrick, even some Republicans say he went too far this campaign by bemoaning an "invasion" of immigrants crossing into Texas. Cruz never backed Patrick but did call Sen. Ken Paxton, who's running for attorney general, a fighter against "Obamacare, voter ID and religious liberty." Paxton is now in a runoff.

Although Cruz made few public endorsements, among them was for Republican Konni Burton, who is running for Davis' state Senate seat and has followed Cruz's lead on various social issues.

Texas candidates willingly went along with Cruz and craved his endorsement.

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.

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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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Follow Paul J. Weber on Twitter: www.twitter.com/pauljweber