I visit that area at least once a week, and I'm willing to bet that most of the cars parked across the street in the "No Parking" zone have government employee permits. If those cars weren't there, the UPS truck would have plenty of space to park.

This is common all over the Financial District: loading zones filled with civil servants' cars, delivery trucks (UPS, FedEx, USPS) parked on sidewalks, pedestrians being squeezed or walking in the street. You could spend a solid 40-hour week taking pictures of all the permit abuse and posting it to unicivilservants.org.

One would be to simply create more commercial loading zones. Less room for private cars, more room for the services that make living without a car easy.

Another would be changing parking laws. Parking on the sidewalk, unacceptable. Double parking, acceptable. This is a quiet side street, and maybe it can stand to be blocked for five minutes. This probably wouldn't work well with Manhattan's long blocks, though.

Three would be to reconstruct this street more in the style of a woonerf or using shared space principles. In short, tear down the curb and pave it all in stones or bricks to make it one huge sidewalk that cars are also allowed to drive on. Put in "obstructions" like bike racks, trees, planters, or public art in a couple places that will cause no problem for pedestrians but cause traffic to slow down to a very slow pace. Pedestrians themselves, who will be using the entire street, will form an obstacle of sorts. It's okay to limit traffic to 5mph on a side street. It's important to remember, though, that you can't accomplish this with speed zones and will have to redesign the street.