I started with an inexpensive Schwinn cruiser also. At first a few miles were all I could handle, due to my poor fitness, and the cruiser was fine. Soon though, I started commuting 4.5 miles, one way, to work and stretching it out on weekends. Much over 8 miles and I found the cruiser very uncomfortable. I bought a road bike and am now riding Approx 80 miles per week for commuting and weight loss.
I'd ride the cruiser as long as it's fun and comfortable. However, if you start getting uncomfortable don't just assume it's you. It may be the bike and perhaps you can try something different.