After the tax return has been Accepted by the IRS (meaning only that they received the return) it will be in the Processing mode until the tax refund has been Approved and then an Issue Date will be available on the IRS website.
See this IRS website for federal tax refund FAQ's - https://www.irs.gov/refunds/tax-season-refund-frequently-asked-questions

If your tax return included the Earned Income Tax Credit and/or the Additional Child Tax Credit and you are receiving a federal tax refund, see this IRS website for information concerning the tax refund - https://www.irs.gov/individuals/refund-timing

I've been checking the website. It has not made any progress beyond stating that it's been received. On Saturday it will be 21 days since I filed. I have one dependant who doesn't qualifyf the child tax credit. I feel like something must be wrong with my taxes and that's why it's been processing for so long. My question was basically asking if it seems likely that they will be rejected and if so, how long does it take to make me aware of it?

Turbo Tax will not know if or when a return will be rejected. If they are, you will be notified. You can continue to check the IRS website for any updates.

Please use this link to track your refund from the IRS.

https://www.irs.gov/newsroom/use-the-wheres-my-refund-tool