No one, not even the IRS, can tell you when you will get your refund. There are many variables that can affect how long it takes to process your tax return and issue your refund. The IRS says that, for e-filed tax returns, they pay 9 out of 10 refunds within three weeks. Yours could be the one out of 10 that takes longer. Go to the following link on the IRS web site for more information about the factors that can affect when you get your refund, and a link to check the status of your refund.
Tax Season Refund Frequently Asked Questions
At some point TurboTax might have showed you an estimated date for your refund, but all it does is give you the date that's 21 days after you file. It's not based on specific information about your tax return, and it doesn't mean that you will get your refund by that date.