Other contenders in Tuesday's primary included former Dallas Mayor Tom Leppert and ESPN Broadcaster Craig James.
CNN: Texas GOP Senate primary heads to runoff
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Today, my colleague Jimmy Leppert highlights how urgency, creativity and the light touch of leadership can yield incredible results.
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"The real trick for Dewhurst is to get Leppert voters to turn out in the runoff, " said Mark Jones, chairman of the political-science department at Rice University in Houston.