What is the time period a President has to act on a bill sent them by Congress?

The US. Constitution limits the President's period for decision on whether to sign or veto any legislation to ten days (not including Sundays) while the United States Congress is in session. If the Congress remains in session and the President does not sign the bill, the unsigned bill becomes law. However, if Congress cuts short this period by adjourning and the President does not sign the bill, then the bill dies. This latter outcome is known as the "pocket veto." Article 1, Section 7 of the US. Constitution states:

If any Bill shall not be returned by the President within ten days (Sundays excepted) after it shall have been presented to him, the same shall be a Law, in like manner as if he had signed it, unless the Congress by their Adjournment prevent its return, in which case it shall not be a Law.