Originally Posted by AndrewP

You need to watch out more for potholes and cracks in the pavement with thin tires, but this is a question of comfort rather than safety. If you have 23 mm wide tires, you could try switching to 25 or even 28 (if there is space under the brakes). If you dont feel too stretched out with your hands on the brake hoods, your road bike should be fine to learn on. If you feel uncomfortable you could have the stem changed to raise the bars a bit and bring them closer while your body adjusts. What make and model bike do you have?