Washing isn't a problem; however, drying can be. Some campgrounds no longer allow ropes to be tied to the trees, hung between trees or for clothes to be hung up outside ones tent or vehicle. We ran into that at Prairie Creek Redwoods State Park where my family was told to take down their "laundry line" almost as soon as they had put it up. There were 7 of us and we had to go purchase one of those fold-up dryer racks for our bath towels, as the kids came back to camp filthy and their mom insisted they have showers every day.

(I like the drying rack better anyway. Unless they can be hidden fairly well, laundry lines can take away from the beauty of some camps.)
Other than that, the longest trip I've been on was 3 weeks; and, like many others, I simply stopped at campgrounds that had laundry facilities.