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The Constitution paints the president's power in very broad strokes. It says the President is: (1) The Executive Power, (2) The Commander in Chief.

As I read it, Congress can authorize War and actions short of War. The execution of that is left up to the Commander in Chief.

Additionally, Joint Resolution SJ 23 of 18 Sep 01 (one week after 9/11) gave the president the following authorization:

Whereas, the President has authority under the Constitution to take action to deter and prevent acts of international terrorism against the United States: Now, therefore, be it
Resolved by the Senate and House of Representatives of the United States of America in Congress assembled,
SECTION 1. SHORT TITLE.
This joint resolution may be cited as the `Authorization for Use of Military Force'.
SEC. 2. AUTHORIZATION FOR USE OF UNITED STATES ARMED FORCES.
(a) IN GENERAL- That the President is authorized to use all necessary and appropriate force against those nations, organizations, or persons he determines planned, authorized, committed, or aided the terrorist attacks that occurred on September 11, 2001, or harbored such organizations or persons, in order to prevent any future acts of international terrorism against the United States by such nations, organizations or persons. http://www.yale.edu/lawweb/avalon/sept_11/sjres23_eb.htm