When will TurboTax allow you to submit your return with the fees being withheld from the refund?

If it doesn't show you that  "pay out of Federal refund" option yet to pay any TurboTax fees, then likely you have forms in your return that are not yet finalized and ready for efiling.  Once all of your forms are available for efiling, then that option should appear.   Do you have a Form 1040 or 1040A return?  If so, it is not yet ready.

You don't have to pay now.  You can skip that area for now and come back in a few days to choose it.

In order to use that method of paying TurboTax fees you must choose to efile the return, and you must choose direct deposit to get the refund.  Also, you must have a USA address.

You can avoid the 39.99 service fee by paying upfront with credit/debit card or a prepaid debit card you can buy in a store.

Federal forms availability dates:

https://ttlc.intuit.com/questions/1908854-forms-availability-table-for-turbotax-federal-products-exc...  

State forms availability dates:
https://ttlc.intuit.com/questions/1908857-state-forms-availability-table-for-turbotax-individual-per...

The IRS will not start processing returns until January 29.  If you efile before then, your return will just sit stockpiled on TurboTax servers until the IRS starts pulling them on January 29 (except for a few test returns pulled early.)   You won't be able to retrieve the return if you notice a mistake, get an additional W-2, 1099, etc.   If you efile at this early point in time and need to change something, you'd have to wait until after January 29 to first find out if your return was accepted or rejected.   If rejected, you could make any change and resubmit.  If accepted, that would require waiting on any refund, then preparing an amended return, which can be a hassle.

Also, if you have EIC (earned income credit, aka EITC) or ACTC (additional child tax credit), the IRS will start processing them on Jan. 29, but will not start releasing those refunds until February 15.  That means people with those types of credits may not start receiving their refunds until around February 27.