Originally Posted by König

Some people like to make a problem out of nothing. Emergency passports are issued mainly for the purpose of returning to a country of citizenship from abroad. Check-in agents probably know about emergency/temporary passports' existence, and if not, then their supervisors should know 100%. So, if I were the OP, I would get a temporary passport, buy a ticket (preferably from a European carrier, e.g., Lufthansa or SAS) and fly home. At a TSA podium, I would just use my Green Card as identification.

Also, it would be a good idea to apply for a local state ID even if there is no need to drive. California ID cards are quite cheap (~$30) and they can easily be issued on the basis of Green Card and SSN. I personally have both a California DL and an ID card. They look virtually identical, and once (just for fun) I even used an ID card to rent a U-Haul truck :-) Nobody noticed the difference. At least the OP could then fly domestically without carrying immigration documents with her every time (i.e., Swedish passport or Green Card).