If an FDIC-insured bank run occurs, when would I receive my insured funds?

As per the FDIC guidelines: as soon as possible, but usually within two days from the day the bank fails.

When can I expect to receive my money?
Federal law requires the FDIC to make payments of insured deposits "as soon as possible" upon the failure of an insured institution. While every bank failure is unique, there are standard policies and procedures that the FDIC follows in making deposit insurance payments. It is the FDIC's goal to make deposit insurance payments within two business day of the failure of the insured institution.
Note: Some deposits that require supplemental documentation from the depositors, such as accounts linked to a formal written trust agreement, funds placed by a fiduciary on behalf of an owner such as a deposit broker or deposits placed by an administrator of an employee benefit plan may take a little longer. The timing of the completion of the deposit insurance determination is based solely on the depositor providing the documentation needed by the FDIC to determine insurance coverage.

Source: http://www.fdic.gov/consumers/ba...