This working paper by Shlomo Angel and Patrick Lamson- Hall, researchers at the Marron Institute at NYU, studies the evolution of population densities in the built-up areas of Manhattan from 1800 to 2010. They combine census data for population with a series of maps, and conclude that time is ripe for a densification programme that could accommodate a larger population with bottom-up actions, without need to use large public- financed schemes. The proposal is essentially a change in the planning regulations that would allow higher densities in peripheral boroughs, as was done before in Manhattan. This would hardly be seen as a contentious issue where I live, as the habit of living in denser neighbourhoods is more common, but would mean a change for many in the land of the single- family home; even if skyscrapers are not a rarity, high rise housing has different cultural implications, as you would loose many freedoms you have being the lord and king of your lot.
There are two interesting videos which show the base data that helped reach those conclusions