Factors are non-market issue such as social welfare programs, incidental wealth (i.e. kids with upper middle class parents, living at home choosing not to work), general attitudes, the difficulty of the labour (outside vs. inside), the relative buying power of the $2 (i.e. in a remote area, it may be possible to have 'micro homes' and get by, and social acceptance.
Wages for undocumented labour might be a hint at the number though that's probably more than $2, my bet is that's somewhere north of $6-8 right now.
My $2 take is 'long view' i.e. we see favelas in Brazil, people will accept that quality of life unless there are institutional pressures otherwise.
Also consider that the unemployment rate does not count those who have stopped looking for work.
Those without any leverage whatsoever, unskilled workers rate will be the 'absolute minimum required to survive'.
Somewhere around $2/hour over the long haul. Millions of people living in tiny, one room apartments, without basic amenities.
We know people will accept this to survive because they do, all around the world.