If a law is passed by the Congress, is there a time limit before which the President must either sign it or formally use their veto powers?
If yes, what happens if they are not fulfilled?
If no, what happens to the law?
The President has 10 days, not counting Sundays, to sign or veto the bill. If he does not take any action within 10 days and Congress is in session, it will automatically become the law.
However, if Congress adjourns and the President did not sign the bill, the bill will not become law, it is known as a "pocket veto".
This is stated under the Presentment Clause of the US Constitution.
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 President vetoes the bill it is sent back to Congress with a note listing his/her reasons. The chamber that originated the legislation can attempt to override the veto by a vote of two-thirds of those present. If the veto of the bill is overridden in both chambers then it becomes law.
Pocket veto are not very prevalent in recent years. The most recent pocket veto was under the Clinton administration.
For the Obama administration, the status of 5 out of the 12 vetoes is disputed as Obama considered them to be pocket vetoes. However, as he returned the parchments to Congress, the Senate considers them as regular vetoes.
Article 1, Section 7, clause 2 of the US Constitution states:
Every Bill which shall have passed the House of Representatives and the Senate, shall, before it become a Law, be presented to the President of the United States; If he approve he shall sign it, but if not he shall return it, with his Objections to that House in which it shall have originated, who shall enter the Objections at large on their Journal, and proceed to reconsider it. If after such Reconsideration two thirds of that House shall agree to pass the Bill, it shall be sent, together with the Objections, to the other House, by which it shall likewise be reconsidered, and if approved by two thirds of that House, it shall become a Law. But in all such Cases the Votes of both Houses shall be determined by yeas and Nays, and the Names of the Persons voting for and against the Bill shall be entered on the Journal of each House respectively. 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.