Any average fit person should be able to easily cycle 100 mile in a day. A Scottish guy has just cycled 18000 miles around the earth in 195 days, he cycled approximately 100 miles a day for 180 days, the other 15 days were rest days or transit days between Continent's.
The funny thing is the food experts said he needed to eat 8000 cals a day to maintain his physical fitness but the only place he managed to do that with ease was as he crossed the US.
Apparently Mark Beaumonts worst day was when he was cycling through Louisiana when he was ran over and then robbed on the same day. http://news.bbc.co.uk/1/hi/scotland/tayside_and_central/7208875.stm
You can view his route and get some info on his bicycle here at http://www.bbc.co.uk/scotland/outdoors/programmes/pedalling_around/map/