The opensource MyWorkSafe is pretty close to what you're asking for. It works like this:
a) Install MyWorkSafe. Configuration is unnecessary.
b) Connect a USB drive.
c) MyWorkSafe asks "Do you want to use this drive for backups?"
d) If you answer "No", then you'll never be prompted for that drive again. If you answer "Yes", then a backup will run automatically every time you insert that drive.

MyWorkSafe is intended to be used with USB flash drives, so it actually prioritizes certain types of files, while skipping other types if there is not enough space on the destination.

Find it at http://myworksafe.palaso.org./

I too have an Asus RT-N16 loaded with TomatoUSB, Transmission, and apcupsd. I thought I could use it as a cheap home NAS, but I was disappointed with how excruciatingly slow access to a USB port hard disk is. From what I've read, no router is able to provide reasonable speeds to USB ports. I thought the RT-N16 with it's fast processor and plentiful RAM would be different, but it's no better. I just recently replaced my cheap-NAS with a cheap but reasonably fast Western Digital MyBookLive.