That question is literally a massive research project and I couldn't begin to answer it here. The best place to start is probably the DOE 20 percent by 2030 report released in 2008.
The US has huge amounts of available wind energy, but constrained supply chain, development, and transmission resources. 20% by 2030 is technically possible but will require huge amounts of work.
Note for those unfamiliar with the field: there is a considerable difference between "X% of electricity use" and "X% of power use" (for the USA, about a 1:6 factor, if I read http://en.wikipedia.org/wiki/Energy_in_the_United_States correctly). That 20percentwind.org site, to me, has the former as a goal.
You have it right. 20 % of electricity use means, that on average power is the same 20 %. When it is blowing in large areas, more than 50 % of electric power is produced by wind turbines and when it's not blowing the percentage may be very small. In Portugal the maximum power share wind turbines have had is 75 %, though only 17 % on average is produced by wind.[1]
This creates two problems:
1) You need to have a lot of transmission capacity, which is used very inefficiently. With conventional powerplants you can forecast pretty easily, where and how much electricity is produced and consumed and you can size power grid accordingly (with backup capacities, of course). With wind power the production places and amounts are all the time changeing and you should have plenty of capacity, of which on average only small share is used.
2) To cover the consumption during non-windy times, you need to maintain backup power plants, which should be able to follow load rapidly. Water power is ideal for this, but as penetration level raises you need also other power plants, gas turbines for example (but who wants to maintain a turbine, which is used rarely...). Also batteries may be applied in the future, but in large scale that is nowadays pretty much science fiction.
http://www.20percentwind.org/20p.aspx?page=Report
The US has huge amounts of available wind energy, but constrained supply chain, development, and transmission resources. 20% by 2030 is technically possible but will require huge amounts of work.