This depends very much on the what paper stock was used to print the cards. There are paper documents far older than the US Constitution (papyrus written with carbon ink dating back to the Egyptian dynastic period?) still in pretty good shape, and paper books and periodicals printed a decade ago that are going to pieces.
Beyond that, the ink (the main point of deterioration in the Constitution and moreso the Declaration of Independence -- which was written with pokeberry juice for ink) can deteriorate as well.
Pokemon cards are/were printed on thoroughly modern paper card stock, but as far as I'm aware no special care was taken to use acid-free paper or archival inks, so while it's a guess, my guess is we might reasonably expect well-stored cards to last anywhere from thirty to a hundred years. Some of the oldest ones are nearly twenty years old now; if you have a few of those first issues, you might be able to estimate better from their condition than I can from first principles.