I think this can happen when you rename the library project out from underneath the dependent project. Eclipse is reasonably good about about updating dependencies in most cases but this one seems fragile.
First try removing and then re-adding your library in Project > Properties > Android > Library.
If that doesn't work try cleaning your projects, exiting Eclipse, and opening the ".classpath" file in your project's root directory. If you see a line that references your library project under a previous name, just delete it, save the file, and relaunch Eclipse. Build the library project and then your dependent one. You may need to re-add the library like I mentioned above. This is what worked for me at least.
Edit note: I also found some stale references in my .project files. They didn't seem to be causing any problems but I removed them too. If you do that, be sure to search for the old name in that file as there was a whole "link" section near the bottom that also referenced it.