If you are a sworn member of the United States military (and thus subject to the Uniform Code of Military Justice) or have to maintain a security clearance with any branch or department of the United States federal government, signing those ill-conceived and ultimately futile "petitions" to secede from the Union is a Very Bad Idea™.
Likewise, if you ever want to honestly answer question 11. j. on any future ATF Form 4473s ("Have you ever renounced your United States citizenship?") in the negative (like you are supposed to), you might want to refrain from signing those petitions as well.
And, really, if you are going to secede, just do it; asking permission from the government from which you want to secede just seems… silly. Do you honestly believe the answer will be, "Yes"?
Looking at the situation academically, however, it is interesting to see how many people are willing to put their names, however meaninglessly, on a document that goes a bit past merely skirting treason. I seriously doubt anything will come of this, but there are some seriously unhappy – and tremendously short-sighted – folks out there these days.