It's hard to find a quality new bike of any type for under $200 and road bikes tend to be on the more expensive side. Worse than that is that cross bikes are typically more expensive than an entry level road bike.
The difference between a cross bike and a hybrid is that a cross bike is essentially a road bike beefed up for offroad use. The term "hybrid" is applied to a lot of different things. Often they're designed for a more upright riding style than a road bike and putting drop bars on one may not work very well in the end.
Some people have been happy with bikes like the new Varsity and the GMC Denali, but they are not high quality bikes just so you know. I also believe they come with 28 mm tires which might be wide enough for your roads. A pothole or two isn't going to kill a road bike, it's really more about comfort. Bad roads and narrow tires make for a jarring ride. Standard for road bikes is 23 mm so 28 mm may not be so bad depending on how rough your roads really are.