I believe the federal government (and notably President Jefferson) did not support the building of the Eire Canal. There were lots of other reasons New York remained larger and grew more quickly than Charleston or New Orleans. Climate, geography and free labor are some that come to mind immediately.
I'd also argue that the Erie Canal actually helped southern commerce generally and New Orleans in particular because its creation helped settle the Old Northwestern territories. These settlers then used the Mississippi river to conduct trade with the south.
In terms of climate New York is significantly disadvantaged in comparison to practically any southern port. Simply put, it's winters are longer and colder making for a smaller portion of the year in which productive work may occur. There are days every December when it is 20 degrees in New York and 70 degrees in New Orleans. Geography is similarly advantaged to New Orleans at the mouth of the Mississippi river. It was the nation's largest exporting port for a better part of the 19th century as a result of this simple geographical fact. New York, by contrast, is located in the northern extremity of the nation. Its only significant geographic advantage is one that it also shares with most other cities on the upper east coast, that being a proximity to transatlantic traffic.
The labor element seems to have been of little consequence in the area of shipping simply because slave labor, and free manufacturing labor for that matter, were at the time employed primarily in production rather than trade. The southern ports had no more difficulty shipping the cotton out than the northern ports did with bringing the manufactured goods in.
The real reason New York grew so much as a port was the 1846 Warehousing Act. It took advantage of the act's provisions to such a degree that it not only outgrew southern city imports - it also outgrew the imports to every other northern city.