If you are making the move to a smaller SSD drive, you will need to delete a few files off of it to make sure the process completes.
A good place to start is by looking in folders such as My Videos (often has lots of very large files within), then My Music (loads of music collected over the years), then My Documents. Once your backup has completed and you have verified the data is properly backed up, then delete the data within these folders but not the folders themselves, as you may need them later.
It is important to note that we don't want to delete applications in the Program Files folder. This is because we also want them to benefit from the speed boost that an SSD has.

I hope this helps!
James Cutt