A former Daily Show researcher has weighted in on this PVRBlog post, detailing the PVR setup used by the show:
When TiVo footage is needed for TDS that day (i.e., every day), the clips are dubbed off to Beta tape and brought to an editing bay. Yup, sneakernet. Sounds like a lot of work, right? It is. I wouldn't be surprised if the show upgrades to a networked PVR system — especially with an imminent move to HD — but I don't know what their plans are.
Re: "I would think if they are archiving all their footage" — They're not. There are already services that do this for them. The show would rather pay for those services than pay for the equipment + staff necessary to reinvent the wheel. The show does have a vast tape library, much of it stock footage provided by the AP et al. — all the stock footage tapes get saved and logged in a database available to everyone in the office.
But since the only way to save things under the current setup is to dub it off to Beta in real time, there is no way to archive all the footage. A lot of stuff does get saved to Beta, particularly major events that are likely to remain relevant. Yet it's not the News Clip Library of Alexandria that people might think.