I checked their embed page (http://www.google.com/webmasters/+1/button/) and I don't see that it requires any API key what so ever, so I assume this rpc_key thing is something private to the API and fetched as the button-JS communicates with the server.
These keys are probably issued with limited time validity, so possibly the script of the OP has already stopped working (I haven't tried yet).
We DO need a real API for this though - if we webmasters do Google a favor and add the plus one buttons, the least they could do is give us a means of finding out how many time the button has actually been used.
Otherwise, this is a bit one sided: We lend Google space, we do the work of adding the button, but we get nothing in return.