A bill that the President doesn't sign can still become a law in the United States due to the system of checks and balances set up by the founding fathers in the United States Constitution.   Any bill that is passed must go to the President for his approval and it becomes a law if it is signed in the White House.  If the President doesn't agree with the bill he can use his power of veto to send it back to the Congress along with his objections.  At that point, the Congress has ten days (not counting Sundays) to reconsider the law, and if two-thirds of the Congress still vote to approve the law it overrides the Presidential veto and can become a law without the approval of the President.  If less than two-thirds of the Congress vote to override the veto then the bill does not become a law.