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But the Cruz campaign has momentum, he said, and the right message on state’s rights and fiscal responsibility.

Mr. Patrick, Mr. Dewhurst and Mr. Cruz can each claim tea party bona fides, Mr. Sullivan said, and a fierce fight for the hearts of the party’s most conservative voters could open the door for the biggest-name GOP moderate in the race, former Dallas Mayor Tom Leppert. And Railroad Commissioner Elizabeth Ames Jones is still in the race, though she has yet to make much noise with her campaign or her fundraising.

Whoever emerges from the GOP primary likely will face retired Lt. Gen. Ricardo Sanchez, 57, a Rio Grande Valley native who is seeking the Democratic nomination.

Mr. Sanchez, who commanded coalition ground forces in the early days of the Iraq war, has been a critic of Republicans since stepping down in the wake of the 2004 Abu Ghraib prisoner-abuse scandal.