To answer my own question, I received the following from the TA at work:

"SAS recommends all their passenger going to the US (concerns following
destinations with non stop flight; New York, Chicago, Washington and
Seattle) to check in at Copenhagen Airport at least 2 hours before
departure. Check-in closes 1 hour before departure! Even passengers with
an electronic ticket must go to manual check-in. This is due to new
rules that hold airlines responsible for passport and visa control."