Update 17 February 2013: The problem described in this post appears to have been resolved.
Google has recently rolled out a new, redesigned message compose user interface, which breaks Send Tab URLs when selecting the option to send the list of browser tab URLs to Gmail. After logging in to Gmail, users are stuck at the screen showing the progress for loading the inbox.
To workaround this problem, switch back to the old message compose UI. This Gmail Help article describes how to do it.
I am holding off on a "proper" fix for this bug until I have a better sense of where Google is going with this new feature.