Heard about these petitions a while back. Not really news, and nothing will really come of it. Though it is quite amusing.
For starters, it is citizens of the states that are talking about removing their state from the Union, not the actual state government themselves. Though to be fair, the Governor of Texas did start the Texas petition.
"These citizen generated petitions [On Whitehouse.gov] were filed just days after the 2012 presidential election."
So in a nutshell folks can sign away, nothing won't really come from the petitions on their own. Currently the number of folks that have signed the petition for Texas to secede is 112,850. The population of Texas is 25,674,681. It and all of the other states are not really in any danger of leaving the United States anytime soon. In all likelihood the folks that signed these petitions don't realize how much the states actually rely upon the federal government to fund many of the programs, jobs, and infrastructure that they take for granted. But I'm not worried about Oregon seceding any time soon.
I mean hell, there is even a petition to nationalize the Twinke industry. On a more amusing note, there is a petition to deport all those that have signed petitions wanting their state to secede from the Union.
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Long story short, several states have filed petitions to secede from the Union. Except, oh wait, no, that's not it. Several individuals have filed petitions for their states to secede from the Union. Non-binding, legally worthless cries...