Biden should call them the fuck out. Immediately withdraw all federal funding, including anything paid for by the government like power plants and highways. Let them suffer until they're willing to play nice with the rest of us.
That would be political suicide and motivate the red states against him for the election. He can point out that he's wrong because of those in a funny way. But actually doing something about it would be detrimental to his election.
Like red states aren't already motivated against him? That's at least 90% of the reason Abbott is even doing this. Give old Joe a no win situation to deal with and take the focus off their abhorrent abortion and other human rights stances. Like, I know this involves drowning children with razor wire but he gets to control the narrative and move the focus off that.
Nothing would take the attention of off winning issues for democrats like abortion than Biden turning the empty threats of a blowhard into a verified constitutional crisis.