C-SPAN removed the Legacy Player, this method no longer works
Step 1: Disable Flash
(If Flash is already disabled, proceed to Step 2)
Using Firefox, enter about:addons into the address bar and navigate to the Plugins section. Next to Flash preferences select Never Activate from the drop-down menu.
Using Chrome, visit c-span.org and single-click the green Lock icon to the left of the address bar. Next to Flash preferences select Always block on this site from the drop-down menu.
Step 2: Log in to MyC-SPAN
Either log in to MyC-SPAN with Facebook or create an account. Alternatively, use username h9i3A6rst and password 84VdrzB8N (if using these credentials, proceed to Step 4).
Step 3: Switch to Legacy Player
If logging in with Facebook or creating a new account switch to the Legacy Player from MyC-SPAN edit.
Step 4: Save Video As…
Right-click any C-SPAN video and select Save Video As…, you will be prompted to save the video to your Desktop as an .mp4.