No, it's not that you need a 4mb line. I know some guys on the Xbox forums are claiming this, but it's not true at all. They're saying it's because of the AI, which is absolute rubbish. If it's because of AI control, why does the Pit mission lag? Right.
There's obviously a bug at work here. If you're getting lag, try quitting the mission, reopening the lobby, and starting over. This has worked for me.
If you look up 'modern warfare 2 spec ops lag' on Google, you'll get loads of hits. People with 16mb lines are having the same problem. Extremely annoying, really, because Spec Ops is absolutely fantastic. :<