If two months, you will probably need to plan it, because you are probably looking at 8000-9000 miles of driving, 20 to 30 days of driving time for a fairly fast sightseeing pace and not including any extended stops.
For me, I can't imagine the loop as anything less than six months, as I am both a city explorer and a wilderness person, so places like southern Alberta, the bare-rock parts of the West need a week or more, and if I am going to cities like Toronto, Montreal, Boston, New York, Philadelphia, D.C., Atlanta, Nashville, Houston, San Antonio all need at least a week. I was in D.C. for three months, free on Sundays, could not get beyond scratching the surface. Four years in Chicago and I have to keep going back. A week in NYC wasn't enough to get started, I would need 10 years to really learn it.
East Coast must-sees for me are Boston, New York, Philadelphia, the museums and monuments of D.C., Jamestown and the Williamsburg tourist complex, Charleston, Savannah, and on the way back, Atlanta, Nashville and Memphis. Three days to a week for each are going to use up a couple months, considering the driving time to get there.
Then working your way back west, Houston and San Antonio are repeated week-long visits for me, Santa Fe and the Taos art communities are "must see" on the way to the Rockies across southern Colorado (choose Pagosa-Durango-Cortez or Pueblo-Poncha-Monarch-Gunnison-Monarch-Grand Junction, or try to do them both) the onto the Colorado Plateau in southwest Colorado, southern Utah, northern Arizona.
Six months to a year, I would wing it. Two months for such a loop, you need a travel planning program to work in times for each stop, how far to move each day, and just a quick pop in and out of each city you might want to visit.
If you are going into southern Canada, May through September for the timing.