If you are using Windows Server 2012 R2, then you won't be able to use the USGS National Map. This really isn't an Esri issue at all, it is a cipher suite mismatch between the Windows OS and the USGS web tier. I mostly point the finger at USGS because it would be rather simple and straightforward to securely allow continued access to USGS National Map from Windows Server 2012 R2 and Windows 8.1.