Well, actually there is such a charge, sort of. But it is not in reference to what was under discussion. The proper charge is "Obedience required to police officers", which is the title of section 542.501 of the Transportation Code. It saytxinvestigator wrote: There is no charge in Texas of "failing to obey a lawful order".
"A person may not wilfully fail or refuse to comply with a lawful order or direction of:
(1) a police officer; or ..."
But what it is really referring to is a police officer directing traffic. I bring it up just to show where the language comes from about lawful order.
As for the rest of the question asked by LedJedi, the answer is that it comes from court cases and not the law itself. SCOTUS has ruled that when an officer makes a stop, he can order you out of the car or to stay in it and similar situational control commands. This is supposedly for the safety of the people and the officer. I know it works for the officer, and having seen a drunk step out of his car into traffic, I can see how it works for the driver also. The most recent of these SCOTUS rulings came last month when the court ruled that a passenger was also under arrest. They used the logic that the officer was in charge and could stop him from leaving "for safety reasons" to show that it really was a detention.
If the person did not comply, he might be charged with either hindering arrest, resisting arrest, or interfering with a police officer in the line of his duties, depending on exactly what he did or did not do.
Hmm, if it is a traffic stop, one of these days I might just have to write the ticket for failing to obey and see what happens. After all, the law does not say directing traffic for a cop (it does for a crossing guard). Nahh, I don't like being a test case, even when I am on the side that doesn't face punishment. One of my goals is to go through my career and never have the Supremes hear my name in court.