State lawmakers from Brazos County were divided on a proposed referendum that would have let voters decide whether to limit some elected officials to two consecutive terms.
Back in March, Senator Charles Schwertner was part of a 27 to 4 vote approving the proposal.
On Wednesday, Representatives Kyle Kacal and John Raney were part of the 88 to 61 House vote defeating the measure.
It would not have applied to either state senators or representatives.
And supporters said it was not a referendum on Rick Perry, who has not announced if he will run for a fourth full term as governor next year.
The Associated Press contributed to this story.