The isolated North American nodes would continue communicating, transacting, and mining among themselves. The world set of nodes would do the same.
At this point you have two possible chains. If communication is ever re-established the fork would resolve itself with the longest chain winning.
Depending on the time-span this could be catastrophic economically because one chain is basically going to be refunded. So if the North American chain fails, everyone that made purchases on that chain would have received goods and services, but then would get all their Monero back once the chain resolves.