I'm using OS X 10.11.2 and I have two external drives (USB) that I've erased (HFS+ Journaled). I upgraded from Yosemite. When I try to create a back up, my MacBook Pro Retina is stuck in the Calculating stage. On both drives. Erased both drive twice.
Only yesterday, I created a new Time Machine back-up on a reformatted HFS+ disk, so it isn't El Capi.
Unless something went wrong when installing it. In your case, it's highly unlikely that two drives failed. And I did exclude the disk from Spotlight indexing (a lengthy process).
Did you exclude the Time Machine drives from Spotlight indexing?