Pic. The story behind it, true or not, is that when photographer David Douglas Duncan asked the solder “If he could have anything, what would it be?” The answer: “Give me tomorrow!”
Was the soldier ever identified?
Best guess: Forrest “Fritz” Heistermann
This website has a bunch of info. It appears to identify the individual as “Fritz Heistermann” in this painfully made slideshow gallery.
Additional searching: actual first name appears to be Forrest, Fritz is a nickname, last name seems legit, along with the connection to the war. Still no corroboration on that photo caption, however.
Archive.org has a copy of a book that contains two captioned photos of Heistermann, on pp. 98 and 276. I recommend downloading the PDF. A cropped version of the photo from the cover you provided also appears on p. 41, but without a caption.
I’m not amazing with faces, but it looks like it could be him. You can decide for yourself, and maybe try to contact the people who run that veteran site if you’re desperate.
I couldn’t find anything attributing the quote, however.
Thanks. That does look promising.