A couple of thoughts:
First, Americans shouldn't be disheartened or frightened by the secession petitions. Partly I say this is because I'm Canadian and have lived through what a real secession bid looks like; also it's just really obvious that the secession petitioners are a bunch of sad wasters, a relatively tiny group who filed petitions online on behalf of a bunch of states that few them live in, the functional equivalent of clueless second-graders threatening to run away from home because Daddy wouldn't let them eat all the chocolate cake they wanted. (The Canadian example is heartening in other ways. Quebecois secessionism was much, much more sophisticated and dedicated than this -- it only died irrevocably when the PQ was co-opted into participating in Confederation and the Parliament -- but it ultimately failed because its chosen scenario was based on fantasies like "sovereignty association" [wherein Quebec would conveniently not have to assume all its own fiscal responsibilities on acquiring independence] and on getting France to somehow mysteriously compel the US into diplomatically recognizing a sovereign Quebec. The moral being that fantasy can carry a "movement" for a long while, but the more reality starts smacking the marks in the face, the harder it becomes to sustain.)
Second, the United States is divided today in a way it hasn't been since the Civil War... but there's a crucial difference. The Civil War sprang from real, irreconciliable economic difference between two major regions: the North, which couldn't afford to allow slavery to expand, and the South, which believed its economic power was nothing without slavery as a vital and expanding force. (Both of them were right in their way, at least to an extent, as the South's subsequent relative poverty once it lost the war it recklessly started proved.) Granted that reality should have told the South of the Civil War era that it could win far more by politics than it could by open war, there was still a far more concrete reason for the open war, however foolish it proved to be.
There are no such irreconciliable regional differences today. There is no compelling reason for the white rural South and western so-called "Empty Quarter" regions to fear today's urban, modern America other than that they have been told that they should do so; in real terms they're actually far more reliant on collaboration than confrontation, in a way that wasn't nearly as true of the antebellum South. Today's division endures only so long as a more-or-less open fraud of a "conservative movement" can keep it alive. The derangements of that movement are just the fantasies sold to them by the party's moneyed base so that it can keep bilking its marks. That's a division that can quite plausibly be broken down -- however vehement it now seems -- without the trauma of war.
Whether it will remains to be seen, but there's plenty of cause to be hopeful IMO.