I also encountered the same issue - this is what i did: I installed the Visual Studio Remote Debugging Tools 2013 (if you have installed already, uninstall it, and also uninstall the one for 2012 too).
After installing it, go to this path in your Surface:
C:\Program Files\Microsoft Visual Studio 12.0\Common7\IDE\Remote Debugger\arm
Inside there should be an executable named msvsmon.exe; run it.
When you start the remote debugger for the first time, the dialog is called Remote Debugging Configuration, so just click on "Configure Remote Debugging" button at the bottom.
Pin the msvsmon.exe to the start screen by right-clicking (or using touch, touch and hold until the menu options appear).
This works for me and now im able to deploy into my Surface RT under Windows 8.1, from VS 2013.