New York recently received a near-record snowfall. It took several days to clear out, and I suspect much of the criticism directed towards the city is due to the public's underestimating the capabilities of systems.
Every system is designed for a "normal" job- a restaurant can serve 50 people an hour, a stretch of highway can allow 20 cars per minute, etc. Send 200 people or 100 cars at the same systems and they essentially freeze up.
New York could build a snow removal system capable of moving 20 inches of snow in 24 hours- but it would be so expensive New Yorkers would refuse to pay for it. They are willing to pay for a 6 inch system, and since that is a typical snowfall, it works most of the time. Residents are also conditioned to what "normal" feels like. When the response is longer than "normal", even though the demand is much larger than "normal", frustration sets in.
In the case of a 20 inch snowfall, the work isn't simply a linear increase (normal times 3) but probably exponential (normal squared or cubed).
Systems have their limits, which are usually budget-driven.