The NYC Water Supply is a marvel of engineering. The history of thw water supply dates back to 1677. The Chase Manhattan Bank is, in a roundabout way, connected to the first public water supply system.

Today, the Catskills remain as the source of water for NYC.

http://nyc.gov/html/dep/html/drinking_water/maplevels_wide.shtml

Fed by gravity, the system is capable of supplying billions of gallons of water every day.

That's the key, though. It's a gravity fed system.

So, that's why you see lots of these in NYC:
http://www.flickr.com/photos/lintbrush/145275022/

Those tanks are used to deal with water supplies in buildings taller than about 6 stories, but in some places, they are needed for any water at all, because of the elevation of the terrain relative to the water supply.

In short, you should have water on hand. In an apartment, this is REALLY REALLY hard to do. One thing that I used to do when I lived in Manhattan in a tiny place on 25th street was to use plastic 2 liter seltzer bottles in the back of the closet. You can actually get some decent amounts of water in multple bottles.