'Tonight Show' Legend David Brenner -- On Death Bed

David Brenner -- who holds the record for number of appearances on the "Tonight Show" with Johnny Carson -- is on his death bed and people close to him say it's just a matter of days.

Sources close to Brenner say the 78-year-old comedian has cancer that has been aggressive ... spreading rapidly.

We're told Brenner slipped into a coma this week ... and doctors don't expect him to pull through.

David sat on Carson's couch 158 times ... and even hosted the "Tonight Show" a few times.

He was also a frequent guest on Howard Stern's radio show.