iCloud.com doesn't have an interface to access your Photo Stream. However there are other ways to access the photos if you don't have access to iTunes for syncing.
The iOS Dropbox app has recently been updated with a feature that can automatically upload all the new photos from your Camera Roll to Dropbox when you open the app. I believe you can even get bonus Dropbox storage for using the feature.
Once the photos are in your Dropbox account, you can access them through the web interface on Dropbox.com or the Linux client.
The AirSharing app ($9.99 on the App Store) is essentially a general purpose file transfer client. It supports FTP, SFTP, WebDAV, Google Docs, Dropbox and more. You can use it to transfer photos from your iPad's Camera Roll (or other albums) to your Debian machine via (S)FTP or a WebDAV folder running on your iPad. If you prefer to avoid a cloud solution like Dropbox, this is probably the way to go.
These are just a couple options, there are certainly others out there (the Google Drive app would probably work similarly to Dropbox, and there are other apps similar to AirSharing).