"The lawsuit from New Jersey was for tens of millions of dollars, predicting environmental harm if traffic gets worse on the other side of the river."
IF that happens it will be temporary: it's the opposite of induced demand. Many NJ commuters will take to the trains and demand that NJ Transit will get the kind of upgrade that New York's MTA will enjoy. There's $9 bn lying around from turnpike tolls, and they certainly shouldn't use that to widen the 12-lane turnpike.