I believe you are using eclipse? You need to import google-play-services_lib as your own Android project into the workspace (not the project). Make sure you copy the copy to the workspace.
Then, make sure you have a folder called libs in your project and import the android-support-v4.jar file so that older phones can use it.
Then right click on your project -> properties -> android -> select your target name, then scroll down to the bottom mouse click, select google-play-services_lib, click OK.
Clean and rebuild.
If it still blushes, then hover over the red line (perhaps right-click for the options), select the project to fix, and select the correct path if more than one. Be careful, you do not choose a path that is in another project in your workspace, but only for the google-play services themselves in your workspace.
EDIT:
http://developer.android.com/google/play-services/setup.html
Copy the google-play services_lib library project into the workspace (the folder where your GCM project is installed). The library project can be found on the following path.
<android-sdk-folder>/extras/google/google_play_services/libproject/google-play-services_lib library project .
Import the library project into eclipse
Choose File> Import, select Android> Existing Android Code in the Workspace, and view the workspace project in the library project. You can check if this is a library project. Right click on the library project. Go to properties. Click Android in the left pane. You will see the "Library" checkbox.
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