Well, not exactly. It would be more accurate to say that enough people have signed a petition in favor of allowing Texas to secede that the White House will have to issue a formal but in no way binding response to the petition, unless it doesn't want to, in which case it won't. Either way, nothing will happen.
So I guess this development is really not as dramatic as the headline promised. I should apologize for that.
As you may recall, as part of its commitment to appear slightly less horrible than the previous gang of criminals transparency, last year the Obama White House added an online-petition feature to its website. See "Trending at the White House Petition Site: Legalize Pot, Abolish the TSA, Admit Alien Contact," Lowering the Bar (Sept. 26, 2011). The administration promised that it would provide a formal response to any petition receiving more than 25,000 signatures within 30 days, and so far it has done so 82 times (although nine of them are to explain "Why We Can't Comment"). The substantive responses have occasionally left something to be desired, as when I eagerly clicked on the response to the petition to "Abolish the TSA" to find that said response was drafted by John Pistole, the head of the TSA. (Let me go ahead and ruin the suspense by telling you he did not announce he was disbanding his agency.)
On the other hand, the administration did release its official beer recipe.
Anyway, The Hill reports that a petition to "peacefully grant the State of Texas to withdraw [sic] from the United States of America and create its own NEW government" has exceeded the 25,000 threshold and therefore should be entitled to a response. It turns out this has suddenly become a popular idea (again), as there are similar petitions (with similar grammatical errors) now pending for at least a couple dozen states, including South Carolina, which you may remember was first out the door in 1860. This time, Texas was the first to cross the threshold (of signatures).
Many of these petitions just contain language from the Declaration of Independence, but they're not all identical. They appear to have been started by a number of different people, all of whom are both deeply concerned about lost liberty and completely unable to use "it's" correctly. (I'm with you 100% on the first one, guys.) Many but by no means all of the petitions relate to formerly Confederate states, but solidly Unionist areas like Michigan and the Oregon Territory are also on the list. Oregon seems to be a little on the fence, frankly. Its petition is careful to say that the country of Oregon would consider itself an ally of the United States (and you wouldn't invade an ally, would you?!), and also notes that if conditions change later, they might be willing to join the Union again. (You get the feeling they'd cave as soon as we embargoed their artisan coffee beans.)
Maybe I shouldn't be too hasty in interpreting this as a desire to secede. I did notice that quite a few of the signatures in favor of allowing Texas to secede were coming from people who don't actually live in Texas. I would guess that somebody from Oklahoma signing the Texas petition has a very different motive.