According to the pilot, during landing following a cross country flight, the airplane touched down and began to porpoise. The pilot attempted to recover, but the airplane bounced twice. After the second bounce, the pilot felt the airplane was about to stall, and initiated a missed approach. The pilot then flew the traffic pattern and landed again uneventfully. While taxiing to the General Aviation parking ramp, he stated that he could not steer the airplane, and the ground guide observed that the nose landing gear tire was flat. An inspection of the airplane performed by a Federal Aviation Administration (FAA) inspector revealed substantial damage to the lower firewall. The pilot reported there were no mechanical problems with the airplane. A weather observation taken about the time of the accident recorded the wind as 253 degrees at 12 knots, gusting 16 knots.