This could be an interesting AH.
Of course, we all know NATO is willing to go in where the UN fears to tread, as in Yugoslavia...and we all know how it nearly led to WWIII...
Well, to try to avoid NATO intervention, perhaps leave Tunisia out, but Libya and Algeria V.S. Egypt could be a fun TL, and in fact one i've been planning on doing for a while. I was also going to put the Tuaregs into power in Mali with Gaddafi's support so they muck in too.
However, if Russian and/or Chinese vetoing of the resolution is the POD (Or some other way of stopping the no-fly zone) then Algeria & Libya V.S. Egypt and possibly Tunisia is the largest i can see this getting without NATO getting involved. In this situation, Egypt could beat Algeria but it would take a while. The tipping point is probably Libya having the home-field advantage, plus Egypt still facing massive decent at home.
So, in short, Gaddafi would likely remain in power but it would be a long and bloody war with his regime not necessarily lasting TOO much longer .afterwards.