I had the same issue. The problem is that pip install tries to use C:\Users(username)\AppData\Local\Temp to unpack. You have to explicitly set those directories to R/W.I still couldn't do it because it was a work laptop and there were some permissions issues with trying to set these directories to R/W. The alternative is to go to your Env Variables, and set both Tmp and Temp to point to a writeable directory such as C:. The installation went fine. I was able to install pip.
The way I stumbled onto this is by not defaulting pip install in my installation. Even though the pip install was failing, the installer was not giving any errors. Removing pip and then trying to manually add it later is what pointed to what was going on.