In Texas, Monday is the last day for counties to receive overseas and military mail-in ballots.
Valenzuela and Van Duyne were competing to replace retiring U.S. Rep. Kenny Marchant, R-Coppell, in what national Democrats saw as one of their best pickup opportunities in Texas.
1 finisher, Van Duyne, has called on the current runner-up to accept defeat.
Neither Decision Desk HQ, which is powering The Texas Tribune's results, nor the Associated Press have called the race for Van Duyne.
"Once again, I will repeat, Beth Van Duyne will be the Congresswoman for Texasā 24th District," Van Duyne's campaign manager, Donald Rickard, said in a statement Thursday.