I am a beginner that traveled solo earlier this year. It can be done and is a thrilling experience. I didn't make it across country, but this was due to my diet limitations in regard to available food (vegan) and not the feasibility of a solo tour. I can give several pieces of advice:
1. As others said, begin a routine of biking daily to increase your distance.
2. Do a 4-5 day practice trip prior to leaving and bring all the supplies that you are planning to bring on the full trip. This will give you an idea of items that you need to add to your gear and others that need to be removed. It also gives you an idea of what amount of food and water you need to stow with you at all times, which, for me, was the biggest impact to weight. You will also gain an understanding of how reliable your maps and cell coverage may be. Reliable maps are important.
3. I would recommend buying an individual GPS system in addition to your cell phone (even if cell has GPS). The cell battery should be reserved for emergencies and I hit plenty of areas in the mountains where I had no coverage and wish I could get a GPS signal. Even ACA maps can have inaccuracies and it can be unnerving if you get lost alone, or are even uncertain if you are heading in the right direction, especially if you are getting tired or fighting the darkness.
4. Study the maps prior to leaving and know your distance that you can travel in a day fully loaded. 70-80 miles is nothing on flat ground but, if you are a beginner, cut this in half or more for mountains. In some more remote areas you may find that the distance between campgrounds is longer than you can travel, which means a more expensive stay at a motel or hotel. Maps like ACA don't have all the motels and hotels in the area listed, only some, so any means of preparation you can do beforehand will make for a better trip.
5. I think the most difficult part of traveling alone is bike and bag security, especially when going into a supermarket or restaurant. I never had a problem, but I did lock my bike up every time and took in my front panniers when the area seemed sketchy.
6. I prefer to travel solo. If you like being alone then you are going to love this trip. If you like meeting strangers then you will love this trip. Having a fully loaded bike attracts attention. I didn't have a concern about safety from people. I did have a concern about problems with my bike and being stranded, especially during long stretches where there were no bike shops. To help offset this, get a bike that is not complex and so is easy to repair, and bring replacement parts and tools.
7. Finally, I recommend bringing a camera (with additional memory storage), journal and a good audio recorder. They are worth the extra weight. I used the audio recorder for recording thoughts as well as the ambiance of each place that I slept.
If you are interested I kept a blog of my gear purchases, practice run and trip here: http://biasedbohemian.com/bike-across-america/