The reactions I get over this "news" is funniest on Facebook, though it scares me that I've run into people who are taking this idea seriously.
For one, the entire plan, assuming this is a serious secession movement and not just an interesting way of getting government's attention, assumes that the majority of the state agrees with whichever Billy Bob submitted the petition in the first place. As has been stated repeatedly, this is far from the case, and will likely remain so throughout this ordeal for each and every petition that's been created.
Two, many of these states, as has also been discussed elsewhere on the boards, are completely incapable of sustaining themselves on their own economies. Texas and California might be able to, but Cali owes too much in debt and Texas... well, they don't exactly have a history of brilliant politicians. The infrastructure may be there, but I'm almost positive the sudden loss of emergency services, military bases and equipment, and federal subsidies for the farmland and oil industries Texas in particular loves to boast will take it's toll faster than the secessionists have considered.
Third: let's assume that, for whatever reason, Texas (to use the most viable and popular example) is simply let go by the federal government. What happens to all the government infrastructure that's left in Texas? Presumably, the military and any emergency service systems will leave, and the border crossings will be abandoned. What happens to the remaining infrastructure? Will Texas have to purchase the bases, facilities, and even interstates from the US (which I sincerely doubt they'd be able to do all at once)? And, if they can't or won't, how long will Texas tolerate, say, armed forces remaining within their borders like some kind of occupation?
Fourth: What kind of foreign policy plans will Texas enact? I doubt the people submitting these recession petitions care a whole lot for "outsiders", so I can't see them putting up with much in the way of immigration, or even being all that tolerant of trade agreements and foreign embassies. Hell, what are they going to do to fill up the vacuum left by people leaving Texas because they'd rather be in America? By my understanding, such a move would nearly empty out all the major cities.
This entire thing is a poorly thought out plan, implemented by whiny man-children who are upset that there's still a black muslim socialist in the white house, nothing more.