A 767 (with at least full load of pax) could probably get to most/all cities in Chile, Brazil, Bolivia, Paraguay, Uruguay, even Ecuador and Peru. May be stretching it (with the short runway) much beyond that. FWIW, DCA's runway is about the same length (and elevation) and narrow bodies can get as far a PHX from there.
I am sure someone will chime in with the official stats, but a 757 full of fuel and cargo (they have an impressive range) might be too heavy and need too much runway.
IIRC, 757s operate from DCA and should be able to travel much of S. America with a full payload.
This is 1,500mi of AEP
http://gc.kls2.com/cgi-bin/gc?PATH=&...avy&MAP-STYLE=
and 2,000 miles
http://www.gcmap.com/mapui?PATH=&RAN...COLOR=navy&MP=