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Results of camera calibration vary

Hi, I have a problem during camera calibration using chess board. I'm using C++ calibrateCamera method to find out the intrinsic matrix. The problem is the fx, fy are varying from 700 to 1100 depending on the distance from camera the cx, cy vary as well. My question is, can it be caused by poor camera quality(using some no-name webcam with resolution 640x480). Can this poor resolution be the only problem??

I need to have really accurate intrinsic matrix and in this case it seems I will need to calculate it by myself:(

Just to be sure for webcam with fixed focus length, the intrinsic matrix should be always the same isn't right???

Thanks for clarification.