President-elect Donald J. Trump promised to undo many of the Obama administration’s most ambitious regulations. But even before he takes office, federal courts in Texas are doing some of the work for him.

A federal judge’s injunction this week halted a Labor Department rule that would have made millions more Americans eligible for overtime pay.

Over the last two years, Federal District Court judges in the state have chipped away at Mr. Obama’s legacy by striking down or suspending no fewer than five regulations, executive orders or actions, and guidelines, including an action that would have allowed illegal immigrants who are parents of United States citizens to remain in the country, and guidance that would have expanded restroom access for transgender students.

The injunction in the overtime case, issued on Tuesday by a judge nominated by Mr. Obama, has many advocates and legal experts concerned.