When Senator Perkins says that the mist is traveling 500 miles a day and will envelop the entire country, the map and his description of the mist indicate that the mist has only reached the western border of South Dakota. South Dakota alone is 380 miles wide: it should take several days for the mist to envelop the U.S.
Senator Perkins at the beginning says that it will take a day for the mist to reach the Eastern seacoast. Paul is listening to that broadcast at the beginning of the episode. However, clearly no more than a couple of hours pass during the entire course of the episode, and the mist reaches Washington DC within that time.
The alien visitor is using the same map prop that the radio announcer does at the beginning of the episode.