This is a laughable joke at secession. Signing a petition will not do anything. The only routes to secession are: 1.) Through the state legislature and 2.) Through armed conflagration.
1.) This will not happen. At least not for a very long time. The States have much more to consider than a few ornery people who mean truly nothing in the long run. Secession will not happen because we hardly the sectionalized states of the Civil War era. Sure, we have our political ideas that are relatively related to our geography, but most Americans are tied to the idea of a strong Union. Most Americans, I'd say, don't even fully comprehend the idea of "sovereign" states. That even if they were to secede, they wouldn't know what to do with themselves. They would fall into disarray and walk back into the Union with their tail between their legs, begging for its support.
Not to mention, a petition will do little. You can appeal to the people all you want, but that will get you nowhere. You would have to convince the legislature--a body of people who have much more to consider than the average person. And it is that step that would certainly not be easy. You would have to convince them that if they did not secede from the Union that they would become the lesser of their other states. And you could not so easily fabricate a lie of such proportions. That is to say... there actually needs to be some grievances to call the federal government out on. As it is now... there is none. The ENTIRE NATION IS IN TROUBLE RIGHT NOW. Not just a few select states. Thus any grievances that could be brought to light could be the same grievances that the whole nation brings upon itself. And what are we going to do.. have all the states secede from the union into another one? That'd just be plain silly.
TL;DR: The states have no reason to secede.
2.) This idea is even more laughable than the first. Good luck gathering a force strong enough to face the U.S. military. A force of it's own citizens, no doubt. And not the war-faring ones either... The ones who preferred to remain in the home country instead of battling. The ones with little to no experience of being a soldier. Then, of course.. if you even managed to amount such numbers... you'd need to supply them. Weapons, food, shelter... That would all be terribly expensive and difficult to acquire. In order to compete... you would need technologies not so readily available to the publicNot to mention that a few red flags would be raised by the feds for the gathering of such munitions required for war and the congregating of the people supposed to make up the fighting force. It would then be at that point that you look down the barrel of a federal gun, muster the courage to give them a big "**** YOU" and pray to whatever you believe in that they just don't blast you right then and there.
TL;DR The U.S. military would be able to crush any pathetic excuse for an army that anyone could throw together at this point.