Simple answer- if you want to meet your potential and run fast (maybe BQ?), then you need to run. Plain and simple, the best way to get faster at running is to run more. The general consensus on the blog is that Runners World type of "run 3 days a week" schedule does not help you meet potential. If you run 3 days/week and cross train 3 days/week, you will be in good cross training shape. Run every day, or at least 5-6 days a week. If you can run 6 miles every day, great. Raw mileage will be the biggest benefit. Doing a tempo/speed workout on only 15-20 miles/week does not seem right to me- I would not worry about speedwork until you are much higher in mileage.
One other note- as you increase miles, don't be afraid if you slow down. An average 2 mile time of 12:30 with only 20 mpw shows you have good speed. But if you are running 40 mpw or up to 60+ mpw, you can't run that fast every day. Run every day for a while at a comfortable pace. Slowly increase mileage. A long run every other week will help. But just slowly build miles as much as you can. Then check back with us in a few months for high mileage advice.
Read Sasha's very good advice:
http://asksasha.com/Running/Top-10-Training-Mistakes.html