CRM 2011 Router Setup Fails on Windows Live ID Sign-in Assistant Install

I have installed the Microsoft Dynamics CRM 2011 Email Router several times, and there is one issue that I hit quite often. During the router install it attempts to install the Windows Live ID Sign-in Assistant. This component often fails to install without much explanation. If you try to manually download and install the Windows Live ID Sign-in Assistant, it fails with a vague error message saying:

Windows Live ID Sign-in Assistant Setup Wizard ended prematurely because of an error. Your system has not been modified. To install this program at a later time, run Setup Wizard again.