Chris, posting this in case it helps you. I was unable to install all but one of todays updates either, with the same error I was getting previously, but ALSO with a second error code (80071A91). Searching for solutions to that second error code found the following suggested fix which WORKED for me and was able to successfully install all todays updates and the previous update we were both struggling with. May not work for you, as my issue was slightly different, but posting just in case and no harm is done by trying it:
Reset the File System Resource Manager if you receive error 0x80071A91
1. Click Start, click All Programs, click Accessories, right-click Command Prompt, and select Run as administrator.
2. In the Command Prompt window you will need to type the following, and press ENTER:
*fsutil resource setautoreset true C:*
3. Note: You will need to replace the C:\ with the drive letter that Windows is installed on.
4. Restart your computer, and then attempt to install the failed update(s).
Fingers crossed for you :)