I would not call CO, WY, ID and MT the Northwest, that usually means Washington and Oregon. The region you are going to is the Rockies and the Inter Mountain area.
That nitpick aside, you should not have any problems with two exceptions: big popular National Parks: Yellowstone, Rocky Mountains NP and Glacier NP. Best to has reservations for those. And the other problem period is national holidays: the Fourth of July mainly. CG tend to fill up then too. And Memorial Day if you are starting in April.
Otherwise you should be fine, we usually call ahead when we are a couple of hours out and get a campsite. And rarely have a problem.
BK+
