We saw similar rallying in the year following 9-11 and the initial invasion of Afghanistan. With the invasion of Iraq in 2003, it became more complicated very quickly.
Yes and no. You have to remember that the draft started some time before the US was actually at war. A lot of people did volunteer, before the declaration of war and after; but many of them knew that the draft was waiting for them if they didn't.
The narrative my wwii relatives give is everyone enlisted. If you didnt there was shame that required an explanation