Only if you live in one of the states in which they have a physical presence. This refers to someone like me, who pays no sales tax to Newegg because they don't have a presence in my state.
Or if you live in a state like I do that has no sales tax. I don't want a new federal tax imposed on my purchases, which is one of the ideas floating around. Having the feds collect a tax and redistribute it is a tempting angle to avoid certain sticky issues of state tax collection across state lines. People who already are used to paying sales taxes might be ok with this, but what about states like mine that are quite opposed to a sales tax? Would my state have an exemption along with due recourse to fight the collection on merchants who might falsely collect it?