The IRS began steps to correct the error on January 6th, with taxpayers expected to see deposits, where possible, within a few days. Unfortunately, we do not have a specific time frame beyond that.
Taxpayers who do not receive their payment by January 15, 2021, and whose status does not show that a check was mailed should claim the credit when they file their tax return after the filing season begins (typically late January or early February, but the exact date is not yet available from the IRS.)
You will find the most current updates posted here: IRS Updates on the Second Stimulus and here: TurboTax updates on the second stimulus. Both of these sites had updates made as recently as January 6, 2020, and will continue to be updated as more information becomes available.