Now to take a more positive approach than my previous post. First of all, I wouldn't leave until about April 7th. People find the weather on the east coast rather unpleasant in March.
Since there really isn't time to make a great plan, I'd suggest buying the maps for the TransAmerica Bicycle Trail. It's logistically easier than the American Discovery Trail. The maps will list services along the way.
Buy a push cart. They will add at least 5 miles to your daily mileage. They cost about $180. Look for bicycle trailers in WalMart. Any of the Schwinn trailers are fine. Look for one with two front wheels if possible. Keep the front wheels covered with a strip Gorilla tape or they will wear quickly. Replace the tubes with self-sealing tubes.
Don't worry about how far you can walk in the beginning. Just don't let anyone walk into injuries. Even 7 or 8 miles a day is fine for the first couple weeks.
Somewhere along the line, you may feel completing the trip is impossible. Don't despair as many people walk impossible distances after a few months.
Don't worry about the west until you get there as you won't know how far you can walk until you get there. If you can't complete the hike across the country, at least have fun for six or seven months.
Don't bring too much gear. The tent should be small and green or grey for stealth camping. Camo tents are stealthy, but arouse suspicion. Most nights, you probably won't use the tent.
Time to watch Twilight Zone reruns on Netflix.