what kind of bike are you going to use? how are you going to spend the nights(under the stars, in a tent, in a hotel)? how fit are you and how much can you do without, both physically and psychologically?
with the long days of summer, it's not too hard to average better than 100 miles per day, and i mean including days of horrendous weather (lightning storms, hurricanes, etc. when you can't ride). You may be able to do better than 120 per day average if you're fairly fit and can consider a tent and stove as un-needed luxuries. that means you put a whole day in the saddle even on consecutive rainy days, eat out of a can, and spend rainy nights under overpasses. unless you are relatively rich of course.
even then, you'll be doing quite well if you can do it in 3 weeks. people who take a month to do it are not poking around sightseeing.
to do it in 2 weeks, you'd have to be a professional athlete. people who do it in raam style are superstars who dedicate perhaps years of training, lots of money, and have support the whole distance.
if you're new to touring, i'd suggest a 2 or 3 nighter first, reduce your baggage, then see what you can do in a week, and then adjust your plans accordingly.
suggestions for equipment would include: an under 2 lb. sleeping bag, a 2 lb. bivy sack, a 1/2 lb. silicone coated tarp, 1/2 lb or less 3/4 sleeping pad, lightweight raingear at about 2 lbs for both top and bottom, at least 1 change of clothes, fork, spoon, cup and can opener (or swiss army knife), tiny towel, bandana, sunscreen, and tool kit. maybe an i-pod. and definitely don't forget a camera, (and keep it dry).
you can save money by eating right outside the supermarket and stealth camping often.
good luck
