How old is the furnace?
Even a small restriction in either the intake or exhaust can cause a pressure problem ( such as a wasp nest).
Did you take the differential pressure across the switch (assuming a dual port switch)?
Enclosed combustion chamber? Typically those have dual port pressure switches and have a bleed port. (pressure change when pinching off line)
A failed heat exchanger can also do this. Have you preformed a combustion analysis?