In the original Star Trek series, whenever the main engines (warp drive) broke down (which was pretty frequent) the Enterprise would only be able to move using "impulse engines" - a low power, sub-lightspeed manouvering system based on a small fusion ram/ion drive.
By inference, someone described as "running on impilse engines" or "impulse power only" is either:
1. Very tired (a.k.a. 'running on empty')
2. Genuinely ill
3. (derog.) Slow and/or stupid.
"Jesus, I've just had to brief the sales guys on the new product.... they're all running on impulse engies up there".
"You want to go for a beer ?"
"No, man, I'm running on impulse engines... got to go home and grab some sleep."