Can I realistically get to a 12 minute mile and a half?

I have until September 6th before my final PT assessment for police academy. This is the first time I've ran in a LOOOOOONG time, so it's been rought getting back into it. I also smoked up until about a month ago, so my lung capacity is kinda diminished. At the initial assessment, I did the 1 1/2 mile in 18:43. I also didn't have actual running shoes (flat bottomed Chuck Taylor's are a KILLER on your feet at that distance). As of right now, I'm running 3 days a week during the academy at distances of 1 1/2 to 2 miles...and we'll be working up to around 6 miles by the end of the summer. My main problem is my calves get extremely tired (heavy legs) after about 3/4 of a mile, and I usually have to walk for a short distance and then start running again. The other day we did a timed 400m and my average was around 2:10, but my legs were killing me afterward and I can't maintain that speed much longer than one lap. What are some good ways to improve my endurance, and do you think I can actually pull off a 12 minute 1 1/2 mile at the rate I'm at right now?