I submitted my federal tax returns via e-file with turbo tax already. Can I still file my state return when they become available Jan. 20th like the site advised ? $$?

A state income tax return cannot be e-filed until the federal tax return that was filed has been accepted by the IRS.  The IRS will not be accepting any type of 2016 tax return until January 23.  You will receive an email from TurboTax when the IRS either accepts or rejects the federal tax return.