Declaration of war

[MASHED POTATOES. VOTE!]

It's been almost 76 years since the United States formally declared a war for the last time and I wouldn't hold my breath for this occurring again anytime soon, but here's the question: is it feasible for the United States to declare war on ISIS or Al Qaeda, both possibilities being discussed, given the former is not a recognized state, while the latter is an organization?

I believe the U.S. declared war on the Pasha of Tripoli during Barbary War, despite Tripolitania not being a sovereign state. But still, it was a political entity, as opposed to mere "organization".

[True Federalist (진정한 연방 주의자)]

Actually, the Pasha declared war on the U.S.

Jefferson insisted that there was no need for a Congressional declaration (Congress had earlier authorized the use of force in certain circumstances) and Congress went along with him at the time.

I'd say ISIL and al-Qaeda fall under the clause 10 power to "define and punish Piracies and Felonies committed on the high Seas, and Offences against the Law of Nations" rather than the clause 11 power to declare War.