March roadtrips in the southwest
So, you'd be driving about 6 hours per day to get this done in about a week? By my quick calculations, it is about 37 hours of driving time.
You will likely run into some snow in the Santa Fe area, around Silver City (possibly), Flagstaff, and then in the high areas throughout the San Juan Mountains of SW Colorado. Unless you arrive right after or during a storm, the roads themselves will probably be in good shape. With a little good weather luck, I doubt you'll have much trouble.