This is what I did to install the December Firmware when it failed to install on mine (joke was on me!). It should also work in your case.
Surface Pro 2 December 2013 Firmware Update Fails to Install
"Even though it might not come in handy for some beginners, there's already a workaround that requires users to follow some steps to correctly install the firmware update.
First of all, you need to open a Command Prompt window by right-clicking on the Start button and then type NET STOP WUAUSERV.
Secondly, go over to C: > Windows > SoftwareDistribution > DataStore and delete the datastore.edb file.
Next, go over to the Start screen, type “disk cleanup” and launch the built-in utility to clean up system files and Windows software updates. The process should take only a few seconds, depending on your hardware configuration and the number of items to be removed.
Next, reboot your Surface Pro 2 tablet and then launch Windows Update once again."