The IRS says 9 out of 10 filers who efile and choose direct deposit will get their Federal refunds within 21 days after being accepted. Some returns are processed fairly quickly, while others require additional processing due to specific items in the return. Some are pulled at random for more thorough investigation.
You said you efiled and have received emails that your returns were accepted. You should also check the efile status from within your TurboTax program, if you haven't already done so, so it will be part of your saved file.
If those showed it was accepted, you can use the "Where's My Refund" tool at the IRS website below to monitor the status of your Federal refund.
https://www.irs.gov/Refunds
NOTE: When using that tool, use only the Federal refund amount, and not any total refund amount that includes a state refund.
The amount to use is on your Federal Form 1040, Line 21a.
To track a state refund:
https://ttlc.intuit.com/community/refund-status/help/how-do-i-track-my-state-refund/00/25571
