Korea wasn't a "war" either, supposedly (police action).
Even if Korea, Vietnam, Iraq, etc. were formally declared wars, I still think they'd be controversial regardless. With the exception of Afghanistan (the initial airstrikes/invasion, not the occupation and nation building that occurred afterwards), it was hard for the general public to understand what exactly the United States stands to gain from that conflict, or how that conflict is in the best interests of the United States. I guess the post-9/11 Afghan invasion was the last time people truly united around the flag (not Pearl Harbor), and it was because that was really easy for people to understand. They hit us, so we're going to hit them.
For the most part, in a post-WWII world and in a post-Cold War world, the national defense strategy of the United States isn't about doing something when the homeland is directly threatened but rather about maintaining a global balance of power/preventing power vacuums that would otherwise be assumed by someone else (Soviet Union pre-1991, China, Russia, etc.). That's just harder for people to understand; it also doesn't mean that everything we've done was the right thing to do though.