If the offset hotline is not telling you anything, hope for the best. But, no promises. You will see a notice on the IRS site later if there is an offset. TurboTax has no way to know if you have an offset.
TurboTax gives you an estimated date for receiving your refund based on a 21 day average from your date of acceptance, but it can take longer.
Once your federal return has been accepted by the IRS, only the IRS has any control. TurboTax does not receive any updates from the IRS. Your ONLY source of information about your refund now is the IRS.
You need your filing status, your Social Security number and the exact amount (line 20 of your Form 1040) of your federal refund to track your Federal refund:
To track your state refund:
https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund
On the IRS site you are also offered the use of an app called IRS2Go
https://ttlc.intuit.com/questions/1901548-why-do-some-refunds-take-longer-than-others
If you chose to have your TurboTax fees deducted from your federal refund, that will take some extra time, while the third party bank handles the refund processing.
https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions
https://ttlc.intuit.com/questions/2840013-does-accepted-mean-my-refund-is-approved
https://ttlc.intuit.com/questions/3397970-path-act-delayed-refunds-for-some-filers