Time machine backup is very slow (new TM drive and large amount of data)
I recently added a 4TB external drive to back up my Mac Pro.  I had about 2.4 TB of data in the initial pass of the backup with TM.  It took about 9 hours to complete.  I'm not sure the initial estimate is accurate, but it does take a very long time on the initial pass.  Once that is done though, the incremental updates are very quick.  

I think in this case you just have to be patient, and don't pay too much attention to the estimate of completion time.