I'm pretty sure all that supporting yourself stuff only matters for people moving here. You're just visiting, the tickets are bought, which means everything is already worked out and everything you're worried about is already settled.
It's a normal vacation trip.
No one is going to count your money, or search your bags for resumes. Just go home with your return ticket at the end of your stay. 
Also, as long as you aren't throwing money at everything you see, $1,000 should be plenty for 3 weeks of food and a little fun here. I used to live on that much per month, even with paying rent.