FORT STOCKTON, Texas -- When candidates need a little extra help winning an election here, they reach out to Candida Rangel, a 72-year-old grandmother who is the acknowledged expert at rustling up votes from elderly Hispanics in this dusty town.

Working for a candidate for district attorney in March, Ms. Rangel collected about 240 absentee ballots from local senior citizens, many of them illiterate Mexican immigrants who don't speak English. One, 79-year-old Zacarias Leyva, says Ms. Rangel showed up at his tiny house on an...