The Publish feature stopped working once I installed Visual Studio 2012. Publish cannot find the prerequisite Microsoft .Net Framework 4 Client Profile (x86 and x64)
I'm answering my own question. The problem went away when I used a different .Net 4 Client setup program. The exe that works for me is dotNetFx40_Client_x86_x64.exe found at:
http://www.microsoft.com/en-us/download/details.aspx?id=24872
The wrong setup program is dotNetFx40_Client_setup.exe which I was led to by following the Microsoft MSDN help topic How to: Include Prerequisites with a ClickOnce Application (Visual Studio 2012) which led me to this link to the setup. I use Chrome which downloaded the web installer which I didn't realize was not the file I needed. Had I been using IE none of this would have happened. I was clued into the problem by this StackOverflow question which suggests renaming the setup program. Instead of renaming it I just downloaded the correct one.