A constitutional amendment by Sen. Scott Lautenbaugh of Omaha would allow voters to decide if Nebraska should license and regulate wagering on the races.
The measure advanced Wednesday on a vote of 25-18, but faces one final vote. The issue would appear on the ballot in November if approved. Lawmakers first debated the legislation last year.
Lautenbaugh says the state has a tradition of horse racing, and the proposal would save jobs.
Opponents say the bill represents expanded gambling.