If it does, it will collapse to a shell of its former self. People in NYC paying $1/day aren't also going to buy the "right" to reread the same articles on the web for only 24-48 hours after publication, and people outside NYC will just bounce over to washingtonpost.com, and read the few important Times articles through Yahoo.
Besides, the site's already profitable. It's much better for the Times to keep it free and allow its influence to pervade, rather like smallpox.