I mean, there is nothing scientifically impossible or not yet possible in the series.
On the other hand, it definitely is fiction and it has a small amount of science.
I'd say it's not science fiction. The "not really possible" element in the series is basically the fact that a nuclear apocalypse happened, which I don't think really counts as science fiction.
There are many science-fiction titles which deal with a post-apocalyptic setting, but given that Jericho was set in the present day, I'd struggle to classify it as sci-fi.
Its hard as Nellius said, but if we consider the Road and Mad Max in sci-fi genre, Jericho will be there by definition.
Sociological aspects of post nuclear trauma were main plot of the series but i love the background plot working around a conspiracy in US Gov. and its definitely a future projection or and alternate history story.