There is an online petition on the White House's website to allow the state of Texas to secede from the United States. If I were the President, I'd set three conditions that would have to be met in order for a state or territory's independence to be recognized. After all, if there is no right to secede, then Texas is still part of Spain and most of the East Coast still belongs to England.
1. A referendum would be have to be held on the matter, and all adult residents of Texas would be allowed to vote on the matter. (Texas likely would have failed to meet this condition in 1861, since that state did not allow women and African Americans to vote at the time.)
2. Anyone in Texas who wanted to return to the US would allowed to do so. (Again, another condition that 1861 Texas would have failed to meet, since certain individuals were not allowed to leave the plantations that they lived on.)
3. Texas would assume a share of the national debt that is proportionate to that state's representation in Congress. Since the Texas delegation makes up %6 of Congress, that would put them on the hook for about $976 billion.
For Texas to leave now, it'd be like if 50 people went to a restaurant and agreed to split the check. And this guy in a Stetson hat keeps ordering steak, and now talks about leaving before the check arrives. (Insert tasteless joke about having to wash dishes in a Chinese restaurant here.)