I'm not in New York,However--Usually not. Most materials and supplies are taxed when you buy them-
So no tax number is needed---
If you are purchasing items wholesale without paying tax at the time of purchase-- then adding a mark up and taxing your customers on the higher price----then you need a tax I.D. number.
This adds a lot of paperwork to your life along with the possibility of fines if you fail to file the quarterly reports.-----Few contractors have tax I.D. numbers for that reason.---Mike----