American Airlines just sent out an email about the new offer from Budget. You can get up to 3000 bonus miles for rentals of 5 days or longer at Budget’s airport locations in the United States and Canada until April 30, 2013. You can access Budget’s web page for this promotion here.
You will receive bonus miles for shorter rentals as well; rentals of 2 days get 750 bonus miles and rentals of 3 days 1500 bonus miles. You need to use the coupon number MUAZ062, when making the reservation, and choose American Airlines AAdvantage as your airline partner.