Unless there’s a last-minute rush to the exit, the high-profile departures of Supreme Court reporter Linda Greenhouse and others won’t prevent layoffs at The New York Times (NYSE: NYT). The paper offered buyouts six weeks ago in the hopes of trimming the newsroom by about 100 jobs without layoffs; the deadline is April 21 for eligible exempt employees and April 22 for Guild members. But in a memo obtained by the NY Observer, AME Bill Schmidt writes: “While we will not know the hard count until that time, every effort to handicap the outcome suggests that we are almost certain to fall short of the number of volunteers we will need. If that is indeed the case, as we expect it will be, we will—regrettably—be forced (to) resort to some limited number of layoffs within the core newsroom. ... Because the voluntary buyout window is still open for a few more days, and because we know many of you might still be contemplating what to do, we urge you to give the offer serious consideration, if you believe there is some financial advantage in it for you and your family. Each buyout we record before next Tuesday reduces the number of layoffs we will have to seek.”

-- NYTCo reports Q1 results Thursday and holds its annual meeting April 22. 

Update: Radar has more on the buyouts. (via Romenesko) One of the biggest losses may also be the youngest—Naka Nathaniel, 35, a web producer and video pioneer for nytimes.com who spent much of the past five years working with columnist Nick Kristof. Among those also leaving: Dr. Lawrence K. Altman, Philip Shenon, Jane Gross and, reportedly, sportswriter Murray Chass.