Typically, IRS 501(c)(3) approval takes between 2 and 12 months, inclusive of likely written follow-up questions. Sometimes it takes a little less; sometimes a little more. Expedited review can be requested if a new organization is being formed to provide immediate disaster relief or if a promised grant is both 1) substantial relative to the organization’s budget and 2) the grant has a specifically- defined expiration date. There is no guarantee the IRS will grant expedited review requests.
One of the primary reasons for the long review period is the amount of time it takes for a particular case to assigned to a review agent. Depending upon the volume of applications being received by the IRS at any given time, we've seen "inventory" periods be as short as 30 days and as long as 8 months.