The IRS is not accepting tax returns until January 29th. After you file in TurboTax your return will go into a 'pending' status with the IRS until they begin accepting returns. Unless your return is pulled early for them to use in their test period, do not expect your return to be processed until the January 29th. 

After that, the IRS states that 9 out of 10 e-filed tax returns with direct deposit will be processed within 21 days of IRS e-file acceptance.