The president himself does not have this power. If he agrees to, along with multiple other countries, it's within his power.
In short, the president has the power to authorize the use by NATO, and by the UN, of US forces, but not to send them by himself.
If you're going to bring up the War Powers Resolution, you may want to know that it says that the president [Obama] must notify Congress within 48 hours, and also must withdraw forces after sixty days if Congress's approval has not been achieved by this time. Neither the Constitution nor the War Powers Resolution forbids his actions at the moment. I believe Candidate Obama, when he said your oft-quoted quote, meant for longer than sixty days. The Iraq "War" lasted significantly longer than sixty days, and troops certainly did not attempt to withdraw by ninety.