The first thing to understand about a civil war, is that the US military is overwhelmingly powerful. So whichever side gets the most military assets is probably just going to win. Straight up.
The military is somewhat split in their ideology, but in general the rank-and-file is conservative, while the top brass is largely liberal. If the soldiers obediently follow their commanders, it's a losing equation for the right. If they mutiny, the end result will probably be chaos. The best scenario for the right is if large blocks of the military break off and join their side. Although the problem is, if they defect, they won't have access to all the equipment that makes them such a powerful fighting force. They will also be very disorganized and ragtag at that point.

But several red states have ICBM's in their territories. If they could seize control, they could create a standoff. In some cases you could see the "civil war" be less of a hot war, and more of a game of secession whereby states and territories vote for independence. If it goes by a party line vote, the right would be locked in by the west coast. They'd have to absorb some of Canada, or otherwise chase some of the leftists out of Oregon or Washington.
It wouldn't be a stable situation and the threat of a conflagration would be high. In this scenario, it would heavily depend on what kind of foreign allies either side can muster.

I think from this line of reasoning, the left has all the advantage. They would have China, much of Europe backing them up, they have the top military brass, they have most of the economically productive cities. The right would be pressed to fight for their survival.
Then again if you read Siege by James Mason (I haven't) one strategy the right could use is simply starving out these cities of supplies. They can't last very long under a blockade, only a few weeks, and you'd only need to block a few major highways for it to happen. Gives the right a lot of negotiating power.