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Leppert faces Texas Lt. Gov. David Dewhurst (R), who has spent much of his own money on the race and led in polls, and Tea Party favorite and former Texas Solicitor General Ted CruzTed CruzCruz: I'd rather have Trump talk to Taiwan than Cuba or Iran Lewandowski: Top Cruz aide advised Trump team before NH primary Five reasons why Donald Trump could be the 'Greatest Communicator' MORE (R). He has trailed both in recent polls. The top two finishers in the state's May 29 primary will compete in a runoff election a month later.

Leppert has some institutional support from around Dallas and has been spending his own money heavily to try to make inroads with the electorate. Jeffress, the head of the powerful Southern Baptist Convention who had backed Rick Perry's presidential campaign, caused a big stir by repeatedly saying that Mormonism was a cult.