Here’s what will happen, realistically.
First off, these petitions are merely that, petitions. The White House promises to address petitions that get 25,000 signatures (and some of these are struggling just to get that many), and their response is going to be a roundabout way of saying, “Heck no.” Mostly because states don’t have the right to secede.
When, therefore, Texas became one of the United States, she entered into an indissoluble relation. All the obligations of perpetual union, and all the guaranties of republican government in the Union, attached at once to the State. The act which consummated her admission into the Union was something more than a compact; it was the incorporation of a new member into the political body. And it was final. The union between Texas and the other States was as complete, as perpetual, and as indissoluble as the union between the original States. There was no place for reconsideration or revocation, except through revolution or through consent of the States.
And it will be squashed and some people will be mad at Obama until a Republican victory makes them happy again. Certainly nothing to secede over.
But let’s assume they do continue to fight for secession. In that case, the national guard is going to roll up and blockade the state in question. We’re talking military equipment. After a while the U.S. will start accepting refugees from the renegade state. Should the state continue to try and secede, the national guard and military are going to roll in. People have guns in Texas and Tennessee, but they won’t match up against tanks and machine guns. The rebellion will be squashed and the people who led it will be sentenced, probably to life or death. Then the state begins reconstruction.
The chances of that happening are nil, though, because these states don’t want to secede.
Having the president you don’t like elected is not a legitimate grounds for secession. If some essential rights were being grossly violated, maybe, but they aren’t. And if a revolution were to happen for legitimate reasons, you can be sure that other nations would stand behind the revolters in the same way France stood behind the colonies. But this is silly, so no one is going to support them. And these states aren’t going to give up federal funding and government programs simply because Obama was elected and not Romney. Can the people of Texas or Tennessee live without social security? What about welfare? A military? What about funding for their budget? FEMA? Medicare or medicaid? Not to mention the 99% of people in the state that want to stay in the Union.
These people don’t want to secede. Not really. They just want a different president, and have lashed out irrationally on an Internet petition because of it.