An historian named Gordon Rhea has spent years researching and writing about Grant's 1864 Overland Campaign and has published at 4 books on the subject.  His book on Cold Harbor has come up with a much different figure, no more than 3,000 or 4,000 total Union casualties for the entire day of June 1st which includes the charges and the preliminaries.  When compared with Lee's casualties at battles like Antietam or Chancellorsville or Gettysburg, it's clear that the Cold Harbor attack was not the disaster history has portrayed it as.