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, $3,000 is probably double what you would need for 3 weeks of food and a little fun here. I live on less than that per month in Omaha, and I can be extremely wasteful with money.