Sessions was on radio talk shows, working to get his supporters out on Election Day. Frost, a 13-term veteran, was meeting with his supporters, urging them to get out their people, and thanking them for their support.
The 32nd District, along with four other Texas districts, was redrawn last year by the Republican-dominated legislature to elect more GOP members to Congress.
Most experts believe Republicans will maintain their grip on the House, but the Texas races will determine how much they extend their grip. They hope to pick up all five of the Texas seats.
The Frost-Sessions race has attracted more than $8 million in campaign contributions, which makes it one of the most expensive congressional races in U.S. history.