There are legal recourses like having a show-cause summons issued against the governor and to haul his butt into court of course. Really the more Texas escalates, the more likely there will be a more expansive ruling against them than the one they have. Texas would be wise to back a pathway or create a passable maze through the wire for Border Patrol to avoid more judicial involvement. I mainly posted because I wanted to obscurely point out that while people think US Marshals are court controlled, they are really part of the Department of Justice under the Attorney General's control (and obviously the AG works for the POTUS so Biden's control)He could.
But he won't. He's a dimocrap which means he's a coward.