the busiest sites we host are not as impressive as the FBI site: one of them has around 4 million sessions a month and 10 million page views; the other is 3 million sessions a month and 5 million page views
the infrastructure is quite small: only 2 servers running nginx, Varnish, Plone and Zope (in a redundant ZRS master-slave configuration), all of this is behind CloudFlare.
on a curious note the busiest site runs on smaller hardware: 4 CPU cores and 8 GB of RAM (each server); while the other runs on 8 CPU cores and 16 GB of RAM.
why? there are 2 reasons, the busiest is a blog and it has only one or two authenticated users adding content; the other is a magazine and has a larger staff (I think it could probably run also on smaller hardware but currently there's an ugly bug on versioning that keeps flooding the disk with empty blob files and we can run out of inodes).
normally they have around 1000-2000 concurrent visitors, but we had spikes in past months of 10.000 concurrent visitors.
unfortunately I don't have access to the number of government portals but I'm pretty sure are quite smaller.