Can a person be detained on a traffic stop in Texas until a search warrant is issued for not consenting to a vehicle search?

Yes.

But an officer will need "probable cause" and a judge's signature to get a warrant. Probable cause is pretty broad - it merely means that a reasonable person would reach the same conclusion given a particular set of facts. Convincing a judge is often a different matter. Judges (usually) closely examine search warrants and may require more facts or that the warrant be rewritten.

If an officer intends to get a warrant, they will probably keep the vehicle and occupants at that location until they get the warrant. In some circumstances where they feel safety is an issue or their search capabililies may be compromised, they might impound the vehicle until they they get their warrant and complete their search.

So, if an officer is threatening to detain someone until he gets a warrant, it could be a bluff. Or, it could be the start of a long wait. The courts have ruled that for a routine traffic stop you can only be "delayed" a reasonable amount of time. This is generally 20 to 30 minutes. If they delay you longer than that anything illegal found cannot be used against you by motioning to suppress the evidence. This ruling stemmed from a guy driving a Cadillac up US59 while transporting 50lbs of pot (sorry, I don't remember the exact case offhand). If you are held for longer than 30 minutes ask if you are under arrest. If told no, ask if you are free to go. If told no, you have an Excellent case for suing them for unlawful restraint; they can also be charged criminally. They cannot impound your vehicle without arresting you first, and that requires "probable cause." By the way, the clock starts ticking the second you begin to slow down as you are then being delayed.