Constitutionally, yes. Could he have made more of a fuss vocally and tried harder to persuade the legislature or locals, yes. The Texas Governor is an extremely limited and weak position, in which he can basically command the National Guard, veto legislation, fill judicial vacancies until election, and use the power of the message.
Considering what this is costing the tax payers, the enormous strain on the system etc, it's begs the question:
Why didn't he?
Let’s see, what are those three branches of government again? Oh never mind the Execitive branch has no responsibility to enforce the laws of the State, they only have the power to pardon, not enforce right?