I hate this type of comparison, but here goes: if you took Wilco, made a young Tom Waits their singer, and forced them to stick to more traditional Blues-based forms, you'd have something akin to Eels.
The subtitle of SHOOTENANNY!--"Everybody Knows These Are Rock Hard Times"--says it all. The album plays like a deep blue depression on a sunny day, pounding along across it's own unique aural landscape. Some of the more fatalistic stuff is hard to take repeatedly, but "Saturday Morning" is stunning and, while most of the rest of the album is sure-fire Alt Rock, there are moments towards the end, like "Numbered Days," which have some kind of late 60s/early 70s atmosphere to them.
SHOOTENANNY! has been in my short stack of CDs for a month now; it's inspiration may not be unique but the effect the Eels create is.