Congratulations! Accepted means your e-file has passed inspection (Social Security numbers are correct, dependents haven't already been claimed, etc.) and the government has your tax return. Consider acceptance as your official government delivery receipt.
As you may have guessed, the government processes tax payments more quickly than refunds.
Direct debits are usually withdrawn on the payment date you specified in TurboTax. If that date falls on a weekend or official holiday, the funds are usually taken out the next business day.
If you're one of the millions who filed around the busy April 15, 2019 (April 17, 2019 if you live in Maine (ME) or Massachusetts (MA) due to Emancipation Day) deadline, the government might not debit your payment until after the deadline due to high volumes. On top of that, it can take your bank a few more days to post the debit to your account.
Don't worry — as long as you e-filed by April 15, 2019 (April 17, 2019 for those who live in ME or MA) 11:59 P.M. local time and selected April 15, 2019 (April 17, 2019 for those who live in ME or MA) (or earlier) as your payment date, you won't get penalized for late payment (rejected returns have until April 20, 2019 (April 22, 2019 for those who live in ME or MA) to re-file or mail the return).
Credit card and check payments are treated similarly; as long as the payment was submitted or postmarked by the filing deadline, there is no late payment penalty even if the transaction posts or the check is cashed after the deadline.
If you still don't see a credit or debit transaction 7–10 days after your return has been accepted, call IRS e-file Payment Services at 1-888-353-4537 or contact your state tax agency, as appropriate.