It's possible to convert the bike to drop bars, but it'll be expensive. Handlebar, tape, cables, housings, stem, and brake/shift levers are all definites. Brakes are a possibility. For new parts, you may be talking over $200 in parts alone. And after all that cost and work, it may not fit terribly well because of the bike's long top tube -- the bike was definitely designed with flat bars in mind.

There are a few much less expensive options you could try, like bar ends that mount to your existing handlebars. You've got the standard ones like these that start under $15. They don't drop your hands down, but stretch you forward a little bit so you're not as upright. And then there are drop bar ends like these in the $20+ range.