I am wondering, if my taxes have already been accepted, if there is a way to expedite the day I will receive it?

[DoninGA]

Only the IRS and your State control when and if a Federal or State tax refund is Approved and then Sent.

Use this TurboTax website to check the status of an e-filed return and if it was either accepted or rejected - <a rel="nofollow" target="_blank" href="https://turbotax.intuit.com/tax-tools/efile-status-lookup/">https://turbotax.intuit.com/tax-tools/ef...>
If accepted by the IRS use the federal tax refund website to check the refund status - <a rel="nofollow" target="_blank" href="https://www.irs.gov/refunds">https://www.irs.gov/refunds</a>
If accepted by the state use this TurboTax support FAQ to check the state tax refund status - <a rel="nofollow" target="_blank" href="https://ttlc.intuit.com/questions/1899433-how-do-i-track-my-state-refund">https://ttlc.intuit.com/qu...>

[PaulGLO]

If you have e-filed in the past 24 hours, most likely, not yet. It can take up to 48 hours for the IRS to Accept or Reject your return. You will get an email or text, depending on how you chose to be notified. You can also check your return status here: https://turbotax.intuit.com/tax-tools/efile-status-lookup/

There's isn't anything that anyone can do to speed up the process. The IRS is working hard toward their goal of 9 out of 10 e-filers receiving their IRS tax refund in 21 days or less after their return is Accepted, unless you claimed an Earned Income Tax Credit and/or an Additional Child Tax Credit and filed before February 15, 2018 .  It takes until the week of February 27 to receive your refund at the earliest in that case.

If you chose Direct Deposit you have already selected the fastest way to receive your refund. 

Other reasons it may take longer are explained in the FAQ below.

https://ttlc.intuit.com/replies/3302084