I don’t think too many “poor people” are driving into Manhattan on a daily basis.
That is true. Most of the city poor live in rundown neighborhoods or in those massive public housing complexes that you see in Harlem, Bronx, Queens, Brooklyn, etc. There are people living here that have never left the city or haven't even been out of their neighborhood in years.
So the tax won't affect them much.
I've been commuting to Manhattan for 10 years, make a comfortable income, but have never once taken my car into the city. I just have no desire to navigate those clogged streets, jockey for scarce (expensive) parking spaces and deal with all the taxis, pedestrians, and bicycles. So the tax won't affect me either (not that I support it).
The commuter rail system here is top notch. I park my car in Westport, CT and take the Metro North into Grand Central. It's actually the most pleasant commute I have ever had because I get to read on the way to and from work, listen to music, or even have a beer (on the way home).
For those outside NYC, the commuter rails are not to be confused with the subway system. Most people riding the commuter rails are professionals making six figure incomes and they are coming in from very affluent suburbs. It is extremely safe on the commuter rails here.
The subway is a totally different world. But even so, it's a great way to get around NYC once you are in it. You just need to be more on your guard in the subways.
Bottom line, taking a personal car into Manhattan is insanity in my opinion. I would never do it.
There are a lot of working poor who commute into New York City in beat up jitneys who are now going to pay more for that ride.