The ACLU faced that treatment. After the organization made its initial request, the Pentagon and other agencies dilly-dallied for months, denying ACLU requests to expedite the process. (Here's a timeline.) In the end, the government only coughed up papers after the ACLU took it to court, and won.
But even that has been just a partial victory. The Pentagon has held onto many documents—"There are far more documents that haven't been released than have," says the ACLU's Jaffer—and the CIA insists that it doesn't even need to confirm whether the requested documents exist, let alone release them. Even in the memos and e-mails that have been let loose, there's a generous use of whiteout. One series of e-mails from the Defense Department has the subject header, "re: potential torture involving Iraqi detainees." The whole thread adds up to four pages, and with the exception of the subject headers, all are now blank.