The date that was displayed is only a WILD guess...so it could be sooner...or could be even much later....only the IRS has any control over when they actually issue it.
____________*Answers are correct to the best of my knowledge when posted, but should not be considered to be legal or official tax advice.*
Yes, you should receive an email from TurboTax that your refund is on its way. If you don't receive your refund by today, you will also receive a follow up email as to why TurboTax was unable to deposit your funds on time, and you will be entitled to receive a refund of the $25 fee charged if applicable.