Haley Barbour had a 60% approval rating (about the white population of Mississippi) last time I checked. One poll has been done, with John Eaves 35% and Haley Barbour 50%, the rest undecided. Haley Barbour is definitely going to win.
The Lieutenant Governer's race is much tighter but the Republican still has the edge. Granted, I hate Phil Bryant, the Republican, much more than I do Haley Barbour. This is the race that I really want the Democrat to win in. Jamies Franks is running about 36%, and Phil Bryant about 40%. The rest is undecided.
An oddity of the Mississippi constitution is that the Lietenant Governer is, on paper, more powerful than the governer, as he has a lot of control over the senate. The governer, basically, just vetoes and gives state addresses, and pretty much has no other power. Both offices, IMHO, are legislative, but they are still referred to as the chief executives... which is clear evidence that most of the people in the US have no idea what the "executive" branch is supposed to do.