Q108. "Who has the power to declare war?"
A. There is a short answer and a much longer answer. The short answer is that the Constitution clearly grants the Congress the power to declare war, in Article 1, Section 8. This power is not shared with anyone, including the President.
The President, however, is just as clearly made the Commander in Chief of all of the armed forces, in Article 2, Section 2. In this role, the President has the ability to defend the nation or to take military action without involving the Congress directly, and the President's role as "C-in-C" is often part of the reason for that.
What this has resulted in is the essential ability of the President to order forces into hostilities to repel invasion or counter an attack, without a formal declaration of war. The conduct of war is the domain of the President.
These two distinct roles, that of the Congress and that of the President, bring up the interesting and important questions: can the United States be "at war" without a declaration of war? If we can, then what is the point of a declaration? If not, then what do we call hostilities without a formal declaration?
The question of the need for a declaration of war dates all the way back to the presidency of Thomas Jefferson. Jefferson sent a squadron of warships to the Mediterranean to protect U.S. shipping against the forces of the Bey of Tripoli. Jefferson's instructions to the squadron were that they act in a defensive manner only, with a strictly defined order of battle. When a Tripolitan cruiser shot at a U.S. ship, the U.S. forces seized the ship, disarmed it, and released it. Jefferson's message to Congress on the incident indicated that he felt the acts to be within constitutional bounds. Alexander Hamilton wrote to Congress and espoused his belief that since the United States did not start the conflict, the United States was in a state of war, and no formal declaration was needed to conduct war actions. Congress authorized Jefferson's acts without declaring war on the Bey.
Not all acts of war, however, need place the United States into a state of war. It is without doubt an act of war to fire upon a warship of another nation. In 1967, during the Six Day War, Israel attacked the USS Liberty, an intelligence ship operating off the Sinai coast. But the United States did not react as though it were at war, even though many considered the attack deliberate (both Israel and the U.S. later determined the attack to have been a mistake caused by the cloud of war).
It may be correct to say, then, that an act or war committed against the United States can place the United States into a state of war, if the United States wishes to see the act in that light. A declaration of war by the Congress places the Unites States at war without any doubt. Absent a declaration of war, the President can react to acts of war in an expedient fashion as he sees fit.