But Frances T. Farenthold, 81, a prominent national Democrat who is known as Sissy and served from 1969 to 1973 as the only woman in the Texas House of Representatives, said she could not forgive Mrs. Clinton’s vote for the Iraq war and was supporting Mr. Obama.

“I’m not going to set aside everything because a woman is running,” Ms. Farenthold said, adding that the state’s tradition of strong women went only so far. “There’s a tradition of having pets, too,” she said.