The president has at least 30 days after the start of hostilities to notify Congress (e.g. BTW, I started conquering Iran last month, hope you like it). It would be wise for a president to secure Congressional support (of at least the principal leaders of both parties) before starting a war, since (as is the current situation) the president will need massive amount of money to pay for the war (self-guiding rockets with lots of explosives and a close to intelligent computer system are very expensive, and the US is running out of them and needs to buy more). and only the Congress can authorize new spending and taxes.
