When I went to the U.S. in January this year, there were separate check-in desks for flights to the U.S.,, and the line grew pretty quickly from the check in desks, all the way to the back of the terminal (underneath security at T3) and then back to the escalator to/from the trains.
The other day I read something interesting on the SAS web site. The info concerns E-tickets, but my guess is that it must apply to all types of tickets.
This is what I found under "E-ticket > Check-in > Manual":
"Vid resa till USA behöver du inte längre checka in över disk utan kan använda automat"
("When traveling to the U.S. you do no need to use a check-in desk. Instead, you can use the check-in machines")

If E-ticket holders do not need to check in manually, why would holders of paper tickets need to use the check-in desks? Can they also use the machines when checking in for flights to the U.S.?