They can wait a long time. He can ask for an examining trial after a couple of months, but this is only advantageous in limited cases. Smaller counties often only have grand jury meetings every so often. It is not uncommon for several months to pass.
Get a local attorney to answer you questions with specificity.
Good luck.
Under Texas Code of Criminal Procedure, Article 17.151, the state is required to be ready for trial in no less than 90 days when the defendant held in jail awaiting trial. The remedy if the state is not ready is for the defendant to get a bond reduction to an amount the defendant can make, and if there is no such amount for the defendant to be released on personal recognizance bond.
This law only applies if (1) there is only one case, or (2) if the terms of the law apply to all cases holding the defendant in jail.
And, to get the relief provided by the law requires filing a motion.
If this is a question prompted by a real case, the defendant should discuss this law with his or her attorney.