The IRS states that most refund are issued within 21 days (business days) if you e-filed & choose direct deposit, some returns can have delays.  States differ on time frames for issuing refunds.   

Once your returns are accepted, only the IRS & State would know when you will receive your refund.  TurboTax does not get any updates regarding the processing of your return or when you will receive your refund.

You can checked the IRS website Where's My Refund for your Federal information?

https://www.irs.gov/refunds

If you have a State refund, click on the following link, then click on your State

https://ttlc.intuit.com/community/refund-status/help