One thing to consider is that there might be a maximum width tire that can go on the bike. Someone at my LBS measured my bike years ago and told me that 25mm tires are the widest I can use. I don't know exactly what he measured on the bike to determine that.

Another thing is tire pressure. Higher pressure means you feel bumps and cracks in the road more and that can make the bike feel jittery. There's a good chance that you can safely lower the pressure in your tires -- most people inflate them to a higher pressure than necessary -- and that will give you a smoother ride.