You start out picking up fliers and newspapers, then radios and TVs, then people, then houses, billboards, etc, then towns and cities, then counties, and finally, possibly, whole states. Your goal is to try and get 270 Electoral Votes in as little time as possible. The "possibly, whole states" bit is because once you start picking up states the game is going to end pretty darn quickly. It might be more interesting to make the player continue to pick up individual counties, scoring a state when they've picked up the "majority" of the counties in it, though that would get easier and easier as the katamari got bigger. It might make sense to give counties a weight based on their population, so there would be big rural counties that would be light and easy to pick up but do awkward things to your shape, and the smaller, denser, high scoring urban counties. Presumably if you did this the majority required would be based on weight/population rather than just the simple number of counties.
This game needs to be distinguished from Katamari Nationalism or Katamari Corporatism of course, in which after you roll up all the counties/states in your own country, you then proceed to start rolling up neighboring countries.