What do I do if the agency does not meet the FOI deadline?
I filed my request on March 31. On April 4, the agency acknowledged my request but did not say when they would respond. It has now been over a month, and I have heard nothing more back from them.
What do I do now?
It is very rare for agencies to meet any deadlines at all. I would be shocked if they had replied by now this fast. I think you can sue at this point but realistically you can wait.
Jack’s pretty spot on. You can also file an administrative appeal, but at the federal level courts have acknowledged that FOIA offices are understaffed and typically don’t do much except in egregious cases. The best follow up I can recommend is to ask them to give you an estimated completion date, which then is a starting point for negotiating about whether you feel its reasonable and might open the door to, for example, modifying your request to make it move more quickly.