If TurboTax provided a date, that is an estimate for the average circumstance. Some returns require more processing time. Go by what it tells you at the IRS website. What is showing in the IRS "Where's My Refund" tool?
https://www.irs.gov/wheres-my-refund
NOTE: Here's one common delay that many encounter this time of year, if it applies to you:
If you claimed the Earned Income Credit (EITC) or Additional Child Tax Credit (ACTC), then by law (PATH Act) the IRS cannot issue a refund on those returns until after February 15. IRS goes on to say that those who claimed those credits should be seeing refunds deposited by February 27, although some filers with those credits may see it before then (but not before February 15.)