Wow! That would be awesome! Can anyone point me to instructions on how to set up an external USB to my router for TM backups, please?
If your router has a USB port, and if it supports the function, you can plug the drive into that port and it should show on the network as a network drive. You find it in Finder by clicking on Network in the leftmost column. Once it appears, you can click on it in the left column to mount it. To mount it automatically, once it is mounted, open System preferences/Users & Groups, then your account, click the lock icon to unlock and then click "Login items" to see what opens when you log in. Drag the drive icon from the desktop (or Finder) to that window and drop it. Or, click the "+" and navigate to it in the resulting panel. Once it's in the list, you can click the lock to lock it in and exit Sys prefs.
NOTE: Some (maybe a lot) of internet providers who provide the router disable the USB port. In that case, this approach won't work. If you still want a networked drive similar to Time Capsule, you can follow LIAB's suggestion about getting a dedicated network attached storage (NAS) system.
And one final option. If you have a second Mac, you could attach the drive to it full time, turn on sharing for that drive and then mount it on the Mac you use and point TM to it. In that scenario, the other Mac is acting as the Time Capsule emulator. I have that running in my network.