The Washington Post reports that Senator Paul “plans to introduce legislation to repeal the use-of-force resolution that paved the way for the Iraq war,” and notes that President Obama supports the repeal of the Iraq AUMF. The 2002 Iraq AUMF authorizes the President to use necessary and appropriate force to “(1) defend the national security of the United States against the continuing threat posed by Iraq; and (2) enforce all relevant United Nations Security Council resolutions regarding Iraq.” Senator Paul appears to believe that repealing the 2002 Iraq AUMF “will ensure that our chapter of action in Iraq is officially closed, and that any future President seeking to engage in the region will be required to come to Congress to gain authorization and support, as is Constitutionally required.”
If this is his aim, and if the main potential magnet for U.S. involvement is al Qaeda affiliates in Iraq, then repealing the 2002 Iraq AUMF won’t accomplish much. The main reason: the President has other authorities, including Article II, the covert action statute, and most notably the 2001 AUMF, which the Executive branch has interpreted (roughly speaking) to authorize the use of force against al Qaeda and associated forces anywhere they are found. In this connection, it is worth studying DOD’s super-broad understanding of what the 2001 AUMF authorizes at last May’s SASC hearing, including this statement (with my emphasis) from from Assistant Secretary of Defense for Special Operations and Low-Intensity Conflict Michael Sheehan:
When I said that [the President] did have the authority to put boots on the ground in Yemen or Congo I was not necessarily referring to that under the  AUMF. Certainly the President has military personnel deployed all over the world today, in probably over 70-80 countries, and that authority is not always under [the 2001] AUMF. So I just want to clarify for the record that we weren’t talking about all that authority subject to  AUMF.
For almost every plausible scenario in which we might “engage” Iraq militarily in the foreseeable future, repealing the Iraq AUMF will not legally handcuff this President or future Presidents. Airstrikes, missile strikes, and drone strikes in Iraq against al Qaeda associates, as well as intelligence operations with boots on the ground (and in other forms) to prepare for such strikes – none of that, as far as I can tell, necessarily depends on the 2002 Iraq AUMF.