Can Obama go to war without Congressional approval?

The Answer is YES.

The President has broad constitutional power to take military action in response to the terrorist attacks on the United States on September 11, 2001. Congress has acknowledged this inherent executive power in both the War Powers Resolution and the Joint Resolution passed by Congress on September 14, 2001.

        The President has constitutional power not only to retaliate against any person, organization, or State suspected of involvement in terrorist attacks on the United States, but also against foreign States suspected of harboring or supporting such organizations.

        The President may deploy military force preemptively against terrorist organizations or the States that harbor or support them, whether or not they can be linked to the specific terrorist incidents of September 11.