How long does it take TT system to update to accepted?

Normally 24-48 hrs.  for accepted status from time of transmittal. Do a check your efile status and it should reveal any delays that could be caused by misplacing information or wrong AGI input.

BUT...since millions of tax forms have been stored up over the past few weeks, it may take a whole week for the IRS computers to weight thru them all...so, likely "sometime" this week.

Later in the tax season up-to 48 hrs is normal, unless the last week before the deadline.

Im not talking about with the IRS. I am able to see that my refund has been accepted by the IRS but still shows pending on Turbo, so Im just wondering how long it takes TT system to show accepted as well. 

Agreed the back log certainly will impact the verification process and the transmittal confirmations . So this year what would normally take up to 24 to 72 hrs will and can take up to a week or more .