My bank was having "technical issues " and I was forced to close my savings account in order to access my funds. The bank told me that this was the only option that I had and that I would be able to reopen the account once they fixed their technical issues. When I went to reopen the account after the technical issues were cleared then the bank told me that federal law requires that I wait 90 days to reopen the account.
I have not been able to find any evidence of a federal law to that effect, although I do not have access to any law-specific search-engine (should such a thing exist), so I cannot say categorically such a law does not exist.
However, it is possible there may be a way of circumventing their restriction.
The question What US law requires a bank to reopen a closed account if a third party sends money to it? on PF&M arose from a credit union reopening a closed account when someone else tried to deposit funds to it (the answer concludes there was no federal law, despite the bank's claims, but for our purposes, that is not important: what matters is that they did reopen the account).
In the same vein, the article Bank Accounts Are Hard To Close, And Even Harder To Keep Closed on the HuffPost website bemoans several banks' policies of reopening accounts if a deposit is received after they have been closed:
Bank of America will reactivate a closed account if an electronic deposit or credit, like an automatic bill payment, is made. "If we receive something, we may reopen the account to accept the item, and the account may be subject to associated fees," Betty Reiss, a Bank of America spokeswoman, told The Huffington Post. "We remind [customers of that] when they are closing the account."
JPMorgan Chase also will automatically reopen a customer's account after it's closed if the bank receives a deposit. The bank, which recently eliminated its policy to charge customers an account-closing fee, indicates in its fine print that "any closed account may be automatically reopened if we receive a deposit to the account."
And finally, from the PDF Rules Governing Deposit Accounts from Fidelity Bank:
Closing an Account. [...] If we receive a deposit to your closed account, the account may be reopened to accept the deposit and funds deposited therein will be subject to any and all rights we may have with respect to offset or compensation.
Although all the above sources treat the phenomenon as a negative, they do indicate that many banks will (or, at least, may) reopen an account if a deposit is attempted into it.
Therefore, you may want to check the terms & conditions that came with your (now closed) deposit account. If they indicate that your bank operates a similar policy, it might be possible to trigger reopening the account immediately by sending it some money through ACH or similar. (And might even work even if they do not explicitly state this).