I'm with NTF on this one, maybe not all the way to 15 mph but definitely 13+.

The ultra cheap bearings and races, cleap poorly lubricated chain, freewheel filled with a glue like substance vaguely resembling grease, and all the rest could be lowering your drivetrain efficiency from 98% to 90%. Simply swapping knobs for slicks is worth 2 mph on top of that. Add another mph for skinny slicks. And although weight is rarely as important as the weenies would like you to think, I get about 0.1 mph for every pound lost. Mal-Wart bike at 35 lbs. -> road bike at 20 lbs. = another 1.5 mph. Drop a few pounds from the waistline and and add riding on a regular basis to your training for a few months and there's another 2-3 mph. 9+1+2+1.5+2.5 and 17 mph could potentially be within reach given a few months. After that it gets tougher. The next 1-2 mph could take a year or more to achieve.

As far as the bike goes, rent one, borrow one, beg one, buy one, whatever. You could be a trust fund child for all I know. Our LBS has been known to rent for a day ($30-$50) and let the renter apply that to the purchase price after the race or even a month or so later.