Can a bill become law without a presidential signature?

Yes. If the president vetoes a bill it goes back to the Congress. If both houses of Congress pass the bill again, but this time by a two-thirds majority, then the bill becomes law without the President's signature. Alternately, the President can sit on the bill, taking no action on it at all. If the President takes no action at all, and ten days passes (not including Sundays), the bill becomes law without the President's signature. However, if the Congress has adjourned before the ten days passes and without a Presidential signature, the bill fails. This is known as a pocket veto.