The Trump-backed candidate, Tony Gonzales, remains just a few votes ahead of Raul Reyes in a race that was too close to call on election night, July 14, when Mr. Gonzales led by just seven votes.
As absentee and overseas ballots trickled in across the 29-county district, Mr. Gonzales, a Navy veteran, appeared to pull ahead to lead by 25 votes early this week. Then Mr. Reyes picked up a few votes on Thursday.
“We’re either ahead 22 or 9,” Matt Mackowiak, a campaign spokesman for Mr. Gonzales, said Thursday night. “There’s a discrepancy in Hudspeth and they went home,” he added, referring to tiny Hudspeth County, population 4,866.
Mr. Reyes, an Air Force lieutenant colonel, had been the underdog, but his campaign got a boost in the form of an endorsement from Mr. Cruz, whose emergence in the race turned it into a proxy battle, of sorts, between him and the president.
Mr. Reyes has hinted that he wants a recount.
But Republicans are worried that could potentially further divide their party in the swing district, jeopardizing a House seat they had hoped to retain after the retirement of Representative Will Hurd.
As the Republicans battle over every vote, a well-funded Democratic nominee, Gina Ortiz Jones, a former Air Force intelligence officer, has emerged as a strong general election opponent in the predominantly Mexican-American district, where she almost defeated Mr. Hurd in 2018.