With that budget, you'll be fine. Transcontinental flights get you at least 5000 miles and only cost 250 dollars. 20 of those equals 100,000 miles at $4,000. it's very possible if you have the budget and time.

You can also do an extended mileage run that runs into the 36-48 hour mark that can rack you at least 10,000 miles by combining transcons and/or doing trans atlantic or trans pacific Mileage runs.