Did you get a 4883C letter or a 5071C letter?
If so, this is what the IRS website says
What happens after I contact the IRS?
"We'll continue processing your tax return once we verify your identity and confirm that you submitted the return. If you did file the return, please know it will take approximately 9 weeks to process it once you verify your identity."
It may not take that long, however. There's really no way to know. There are some threads in this forum where other users are discussing 4883C and 5071C letters and their experiences with time frames, etc. So you can use the forum search to find one of those threads if you want to discuss it with some of them.