SANTA CRUZ, BOLIVIA -- A television ad that has aired around the country opens with a photo of Bolivia's leftist President Evo Morales dressed in the garb of a traditional shaman. An image of Jesus Christ arrives to knock Mr. Morales off the screen, and a document labeled "New Constitution" appears amid flames. "Choose God. Vote No," the ad advises.

The ad, funded by an evangelical church based in this stronghold of the political opposition, points up how religion is playing a growing role in the latest chapter of Bolivia's...