After you file

No one can know exactly when your funds would be deposited.  There are too many variables including differences in bank processing times once the IRS sends the funds.

The IRS says 9 out of 10 filers who efile and choose direct deposit will get their refunds within 21 days. 

Some returns take longer for additional processing due to specific items in the return.  Some are pulled at random for more thorough investigation.

Once efiled, wait 24 hours after acceptance, then you can start to monitor it with this IRS tool:
http://www.irs.gov/Refunds

NOTE:  If you choose to pay any TurboTax fees out of your Federal refund, that is another link in the chain, since your funds go first from the IRS to an intermediary bank where the fees are subtracted.  Then that intermediary bank sends the rest of the funds to your bank in a second direct deposit.