Why not ride DAL (or AA or CAL) to EZE from the US? Do you need to go through SCL first?

Also, make sure you're aware of the visa requirements for Chile and Argentina. Argentina just added the visa requirement for US citizens within the last 2 or 3 years. I believe Chile has required this for awhile. The cost of both visas will significantly overshadow the $45 fuel charge you're worrying about.