Question: what happens if the president doesn't sign a bill within 10 days and congress is in session?
Answer: A bill becomes law if signed by the President or if not signed within 10 days and Congress is in session. If Congress adjourns before the 10 days and the President has not signed the bill then it does not become law ("Pocket Veto.") ... If the veto of the bill is overridden in both chambers then it becomes law.