An A320 Captain reported finding the left rudder travel mushy and would not reach the full pedal deflection during flight control checks on taxi out. The First Officer's left rudder pedal had the same problem. Captain notes he had recently experienced a similar left rudder pedal problem in an A319.

Narrative

During flight control checks; I found the left rudder travel mushy and would not reach the full pedal deflection; the right rudder was operating normally and deflecting fully with the pedal. The FLT/CONT (ECAM) page confirmed that there was not a full left deflection attainable; but fully attainable on the right rudder.I stopped in the non-congested taxiway and called Maintenance with my cell phone. Explained the problem and they put me on hold; as it was taking a long time I hung up and called the next Airbus Maintenance number. As I finished explaining the problem; the line went silence... I called Dispatcher and he was having problems calling; we thought there may have been a power outage; so I told Dispatcher that I was going back to the gate since I knew this A320 was not going to fly with this problem. Dispatcher sent me an ACARS message reading: Captain...CALL ME BACK...AIRBUS MAINTENANCE IS SHIFT CHANGING...THEY HAVE THEIR PHONES TURNED OFF UNTIL THEY BRIEF THE AFTERNOON SHIFT WHAT AN AIRLINE. Local Contract Maintenance came over and upon performing a few different hydraulic checks with the flight controls he concluded that this was above his pay grade; but we both have the idea that there might be a hydraulic servo issue in the left rudder system.I am amazed that this company would have such a procedure in place in shutting down phone line communications; or for that matter even ACARS communications; during ANY shift change in the middle of anomalies and maintenance issue in flight; or outside the gate in the taxiway; with an aircraft full of paying passengers!