If you start in May, east to west might be better. Some years, the passes in the Rockies aren't clear until the 1st or 2nd week in June, so west to east in May could be be iffy.
Crossing in 8 weeks might be ambitious for a first trip. But you have to decide on your own personal balance between riding and stopping to smell the flowers. Average daily distances on tours range all over the map. Two likely routes would be Adventure Cycling's Northern Tier (4,280 mi) or their TransAmerica Trail (4,246 mi). To make that distance in 8 weeks you would have to average 75 miles/day with no days off [4250 mi / (7 days/week * 8 weeks) ]
A woman in my bike club made a supported ride across the country on a 3,480 mi modified TransAm route in 30 days (
http://www.pactour.com/north.htm ). She averaged 116 mi/day, but she is a former collegiate runner who trained a whole year to prepare for the tour. Here is a blog from a guy who made a modified east-west TransAm in 8 weeks (
Biking across the USA ) He took a day or two off, but rode some 100 mi days to make up for it.
A more typical average mileage would be in the 50 to 60 mi/day range and would allow for periodic days off. 4250 mi averaging 50 to 60 mi/day means 70 to 85 days on the bike. Just maintain that average every day and you're done 10 to12 weeks. You'ld probably want to add some days off to that. Check a few journals at
http://crazyguyonabike.com for ideas on what daily distances other people have done.
Lately, my wife and I have going on 1 to 2 week credit card trips that average about 45 mi / day. These days 60 mi is the max we can ride in a day and still be ready to ride again the next day (barely).
