This is one of the biggest annoyances I've seen in Visual Studio 2012 and today I finally could find a working solution.
Issue: your Publish Profile is configured -for Connection- to use "File system" and when you try to publish, the files aren't copied.
Probably you got the project from TFS. Your colleague(s) can normally publish the files but the publish does't work for you. Quite frustrating, huh? Don't panic.
Right click on your project. Click on "Publish" > Profile (first tab) > select the profile you need > click on "Settings" > the configuration is probably "Release".
If this appears to be right: select "Debug", close (save) then go back and repeat the same steps and select "Release", then save. It should work.*
If this appears to be wrong, e.g. you have a configuration called "DEV" or "STAGE" or "LIVE" (as I do), select the appropriate one. Then publish. It works (tested).
Check the question Visual Studio 2012 Web Publish doesn't copy files (see comment by firepol) on stackoverflow.
*See the most voted answer besides the "accepted answer".