Time Machine and OS X is tuned to throttle the IO and possibly the CPU usage of the backup task. You can do a few things to modify that behavior - but from the speed benchmark and my experience - a 12 to 48 hour initial backup is not abnormal or indicative of slow backups once you have a few intervals backed up.
- You could log out and minimize other apps / changes to files to let the initial backup complete unhindered.
- You could interrupt the backup, erase the backup destination and tweak the io throttle settings and measure if this helps the initial backup.
To do the second, you'll ned terminal and want to review this excellent answer as well as some speculation on the web.
tmutil removedestination DEB58ECE-531B-4295-85B4-82FC905A01EA
echo 'debug.lowpri_throttle_enabled=0' | sudo tee -a /etc/sysctl.conf
At that point, you would restart your Mac. When it restarts, then erase the USB 3 drive and establish it as the backup destination and start the initial backup again. There's no need to use the
tmutil commands over the Time Machine preference if you like mouse control or visual feedback over terminal commands. The echo 'debug.lowpri_throttle_enabled=0' command needs to be run in terminal, though.
Lastly, you will need to change the removedestination command to command removal of your destination's unique ID instead of DEB58ECE-531B-4295-85B4-82FC905A01EA. Also, you might also see if your current backups are throttled and how they are doing work with:
sudo fs_usage backup
Unless you're really interested in analyzing the low level performance, I'd say you don't have a problem - just a slow initial experience - and revisit things in a week once the steady state backup timings are known. If you get hourly backups completing in 5 minutes or less - you probably shouldn't disable the debug timings as I listed above.