again, I don't understand what problems in the country of departure have to do with Argentina?
They have nothing to do with Argentina.
You might also be searched by Interpol and be arrested trying to get on a plane.
Or you might lack money to buy a plane ticket.
This has nothing to do with Argentina as well.
You can leave the US without passport via canadian land border (if you have enhanced driver's license).
Or you can try leaving in a private yacht or private jet.