They won't be able to ignore THIS volume of e-mail. Trust me.
During the impeachment of King Billy when e-mail was also at a very heavy load, that's the information I was getting from my friend (whom I've known since high school) who works as a high level staffer in Hastert's DC office. This is a widely discussed topic amongst the staffers network.
The office staff worker who answers phones also has to make notes on EVERY single phone call received, and they're usually tallying ayes and nays (that sort of thing) for the topic discussed as well. Likewise, same goes for hard copy, especially HANDWRITTEN letters that don't look like form letters or mass-printed petitions, etc.