No, they really couldn't, it isn't the nineteenth century anymore. And no, there isn't a special provision allowing Texas to secede from the union, this is a popular myth[0]. And as much as Texas likes to believe in its fierce independence, the state is politically, culturally and economically enmeshed in the rest of the Union and without the resources, finances and status of the US (much less the USD,) Texas would be better off rejoining Mexico than trying to survive on its own[1].
I really have no skin in this game, but there are a lot of perfectly functional countries with fewer than 28 million people, and it seems kind of silly to assert that an energy-exporting rich country of 28 million could not survive on its own.
