It would be very hard to have a civil war. For starters, the state militias are all Federally run, and include a handful of volunteers (most of whom are more likely to be red than blue); in 1861 the militias included most able-bodied free white males and were totally equipped and trained by states.
The economy is totally integrated. Without the “red” states, the bi-coastal regions would starve (you do really that almost all food eaten in Brooklyn is grown elsewhere); in 1861 most food was produced locally.
Also, most red states have large pockets of blue, and vice versa. In 1861, virtually no one in the north favored the south (a “dove” simply wanted to let them go), though many if not most southerners favored the union, a factor which crippled their war effort.
One might have to deal with domestic terrorism. For example, if the Democrats try to prohibit parents from giving a religious upbringing to their children (in the best interests of the child), it would probably lead to violence, but not a full war (think of Northern Ireland’s “troubles” or Lebanon as it normally is).