First, you have to postulate a state getting so fed up with the situation to want to leave. Then you have to assume there was no way to remedy the situation without leaving. This would probably require one state getting more pissed off than the others, who stay happy. Why? Because if all the states are equally pissed off, they could make changes through legislation. Duh. If Congress fails to act despite the ire of citizens across the country, then it’s time to replace them. Apathy, schmapathy. If you think your state is getting a raw deal at the federal level, get into politics. Write your reps and senators. Join political groups. Raise public awarness. VOTE. Run for office.
Okay, tirade over. Let’s assume Texas gets pissed off but all the rest of the states are happy. Could Texas leave? I don’t know if there are legal methods in place, but if not they could be created. However, you have to get the rest of the U.S. to agree that Texas leaving is okay, because if they don’t agree it could get testy.
Things like the welfare state, highways, schools, things dependant on federal money would not be a hindrance. Texas wouldn’t pay any tax money to the U.S., so that money could be redistributed within the state. Assuming an amicable break up, trade would not be stopped. If it weren’t amicable, then Texas would look to international trading partners, and probably find someone willing to provide what they need.
I don’t think Texas would immediately start thinking “Who do we invade?” Come on. Issues with Mexico might arise, but I don’t see it leading to war, certainly not a war to take them over. There might be some incentive to rejoin with Mexico, though given their economic state, I doubt it.
Frankly, I don’t see it happening. Despite the militia groups and Republic of Texas folks, most Texans are happy to be U.S. citizens as well, and regard those separatists as the loonies they are.
Could there be war if a state tried to leave without permission? Yes. But the reasons go to why that state is seceding and how they are going about it. Grabbing a bunch of guns and saying “We’re independent now!” ain’t going to do it, and will (rightly so) be seen as a coup by a bunch of nuts and will require intervention. If a state is sincere about wanting to leave, they will seek formal, diplomatic means, including a state referendum for starters to make sure the citizens of that state are in agreement they want to go. That’s not something the governor or state assembly can decide. If it got that far, then the U.S. gov would have to start taking it seriously. And if they got that far, then using the DoI as a source would be legitimate.