Nicely comical, if a bit controversial.
The US would cease trade with Texas and set up an embargo in the gulf. There wouldn't be a need to invade. We'd let you sit behind your border guards and just wait while all your cars and home theater equipment became obsolete. About the only thing we'd let through the embargo are your magazine subscriptions so you'd know about all the latest/greatest cars and home electronics you wouldn't be able to get your hands on.
The citizens would revolt, beg to be let back into the Union, and the Republic of Texas would cease to exist.
