No, Texas is too much of a threat, so it would be a high-priority target for other states. After the strongest states have weakened or destroyed each other, the weakest states, which had been ignored, would then be free to clean up.
Assuming no alliances were formed, which is a big assumption, the final survivors would be Colorado, Alaska, and Pennsylvania but not for reasons you might think.
Colorado, stuck in the middle, would be mostly wiped out early on from all sides, except for a handful individualist mountain-folk survivalists hiding in the mountains.
Alaska, too far and too underpopulated to have been considered by any other state, will have pockets of survivors scattered all over.
Pennsylvania, like Colorado, will have been wiped out early on...except for a couple of Amish farms, whose inhabitants:
1) Weren't aware of any kind of war;
2) Quickly dominate the area, since they've been living in a post-apocalyptic setting for 200 years and are used to it.