There are apparently a couple of ways to see this issue. One is, if you upgrade from Windows 7 to Windows 8 after you've installed Visual Studio 2012. This is described in KB2738090, "You cannot build a C++ application for Windows Store after you upgrade to Visual Studio 2012 and upgrade from Windows 7 to Windows 8" (apt, isn't it). Answer: Repair your VS 2012 install.
The other way is if you install Visual Studio 2012 Update 1, and some confluence of stars causes some of the core library to be uninstalled. If your %Program Files%\Microsoft SDKs\Windows\v8.0\extensionsdks\microsoft.vclibs
directory has gone missing, you may find as I did that no amount of repair, removal, and replacing of VS or the Windows SDK can bring it back.
A little sleuthing led me to a couple of registry keys that appeared to be preventing the core library from being reinstalled:
HKLM\SOFTWARE\Wow6432Node\Microsoft\VisualStudio\11.0\VC\Libraries\Core\ArchNeutral\PaddedVersion
HKLM\SOFTWARE\Wow6432Node\Microsoft\VisualStudio\11.0\VC\Libraries\Core\x86\PaddedVersion
When I set both these REG_SZ values to "0" instead of "51106" and then reinstalled VS 2012 update 1, the extension SDKs for the core libraries returned, and I could once again build C++ Windows Store apps.
Perhaps this will help someone else who lands here after some searching for this apparently rare problem.