If he doesn't declare war, he's limited to like 6 weeks or some shit before he has to request Congressional approval.
The question is, if a president engages in those types of strikes, and then Syria/Iran launch missiles at Israel, is there any Congressman or Senator who wouldn't, at that point, vote to authorize war, excepting the absolute most vehemently anti war like Bernie Sanders or the most intransigent anti Obama Republicans like Cruz and Paul, the latter of which I could actually see voting for war at that point as well, even if it was something they'd have to agree with Obama on.