Hi Joe.
A car woofer was designed for the volume of space in a car and the electrical requirements from an automotive power system. While it IS a subwoofer, the target environment is very different so I'm not sure the results would be good.
There is a lot of science involved in driver-size, enclosure and room size for a sub. The actual driver may not be the most important (or expensive) part.
Building your own sub is a good way to get a great subwoofer at a budget price. (Tom & Ron of SVS started out helping people design their own subs.) But you might want to try a kit first. Check out some of the DIY subs from
www.partsexpress.com or do an internet search.
Hope this helps.