Not necessarily. You do need to capture enough images so that the target is seen in all portions of the camera image area, but you don’t need to fill the full camera image with each calibration image.
I would try to print a target as big as you easily can (maybe a 11x17 or A3 paper size, and do your best to make it flat. Gluing to a piece of glass or similarly flat substrate is helpful - cardboard / wood tend to bow, and the bowing can affect accuracy.