I just received an email from the Minerva project at the Library of Congress asking permission to archive parts of my site related to some recent historical events.
This seems to be a legitimate project.
My biggest concern is will this have a negative impact on my site (the original) in the long term. In other words, is there a chance that Google might see the content on the LOC archive and think that my site is the duplicate?
You should ask them more about their intentions and whether they have thought about how to handle the duplicate content penalty. It's something they will have to contend with sooner or later so you might as well ask them if they have thought about it.