Anthony Weiner -- 2 Homeless Guys, 1 Dollar -- WHAT DO YOU DO???

New York City mayoral candidate Anthony Weiner found himself in a compromising position yesterday -- two homeless guys asked him for money ... but he only had ONE dollar bill remaining.

Weiner -- who was leaving Nello's -- DID have a wad of larger bills, but A.W. made it clear ... George Washington was the only president he was willing to part with.

In the end ... only one guy got Weiner's dollar. The other guy -- well, he got the shaft.