The pressure now moves to the House, which is in recess, as the government enters at least a limited funding lapse.
Follow along for live updates in the runoff election between Democrat Taylor Rehmet and Republican Leigh Wambsganss.
Whoever is elected will fill the northern Tarrant County seat, previously held by Acting Texas Comptroller Kelly Hancock.
It's vastly different from the record 43-day federal government closure in the fall, but some agencies will be affected.