I just deployed an asp.net mvc 3 web application to AppHarbor but it failed:
C:\Windows\Microsoft.NET\Framework\v4.0.30319\Microsoft.Common.targets(3932,5): error MSB3541: Files has invalid value "<<<<<<< HEAD". Illegal characters in path. [D:\temp\q5cmde4m.uk1\input\MyProject\MyProject.csproj]
This happened after I opened the project with Visual Studio 2012 (the application was created with VS2010).
Try to search the entire solution for the value and remove it from where it occurs, and then delete the obj folder from your project. When you build again it should work.
The obj folders are hidden in Visual Studio. You can see them with a file explorer.