Can I choose to just pay my state taxes at this time, and come back and pay federal?

Do you mean to pay the tax due?  You can fill out the federal and state returns.  Then say to mail state and pay the tax due by check.  You don't have to pay the federal tax due first.  

You cannot pay or file state returns independent of federal returns in TurboTax Online.  You can choose to only file and pay for federal, but this is not an option with state.  https://ttlc.intuit.com/replies/4232481