At this MS forum post Brad Sullivan the Program Manager for Visual Studio Debugger has posted the following:
There is a known issue in the installer for Remote Tools for Visual
Studio 2012 that is breaking remote debugging on Windows Server 2008.
While we work on this issue, you can use the following work-around:
1) If not already, please install “Platform Update for Windows
Server 2008 (KB971644)” from Window Update. It will
install KB971512, KB971513, and KB960362 in “Control Panel -> Programs
and Features -> Installed Updates”.
2) Install Windows Live Essentials from
http://go.microsoft.com/fwlink/?LinkID=255474
Following these instructions should prevent you from seeing the error
regarding Windows Web Services API.
As odd as it sounds, I can confirm this to have fixed the issue for me.