I'm somewhat conflicted about the whole thing.
On the one hand, I consider myself a patriot. I believe in the constitution, federalism, and the character of the American people.
On the other hand, I seriously do not like the direction the country is taking. I think the character of the nation is still strong, but it's getting weaker. Both parties are reckless when it comes to financial matters, people care more about handouts and less about self-reliance, people want to silence offensive expression instead of protecting it, and don't get me started about attacks on the free exercise of religion.
It's unwise for any of the 50 states to seriously consider secession right now. However, I will not say that the day won't come within the next few decades when it would be wise. The U.S. government is not America, the American people are. If it comes to pass that the U.S. government becomes truly and irrevocably detrimental to freedom and justice, I believe it will be the duty of American patriots to seek its dissolution. If this must happen on the state level, so be it.
Now before you crucify me, let me also say that the Civil War was the single biggest mistake in American history, and it absolutely must not happen again. In order for secession to be morally justifiable, it must happen peacefully. Also, only those states who could support themselves as a country (Texas and California come to mind; others would be forced to collaborate) should bother in the first place (remember this is all hypothetical, none should try it now). In other words, even if secession ever becomes morally justifiable, it will remain mostly unfeasible and unlikely.
So no, I'm not in favor of the petitions, but I do sympathize with the general idea. I'm a patriot to the American people and the American ideal. If the U.S. government becomes an enemy to either of those, then I will be its enemy.
(And as for the recent election, I voted against the president, but I settled on my feelings about secession during the Bush years.)