Texas Gov. Rick Perry (R.) may have defeated Sen. Kay Bailey Hutchison in the Lone Star State’s GOP gubernatorial primary, but he still has a race on his hands, thanks to Democrat Bill White, a former Houston mayor, who’s climbing in the polls. A new Rasmussen survey shows Perry holding onto a four-point lead, 48 percent to 44 percent, against White.

Perry had led White by six points during his contentious battle with Hutchison. Things have narrowed since. “Any incumbent who earns less than 50 percent support at this stage of a campaign is considered potentially vulnerable,” concludes Rasmussen. Still, Christy Hoppe at the Dallas Morning News isn’t entirely convinced that White is closing the gap:

It’s early. And this poll has a substantial margin of error of 4.5 percent. But if you believe it, White is still within striking distance.
The poll also shows that most folks think Perry is doing a pretty good job as governor: he hit the 59 percent favorable. That’s good for an incumbent. But the downside of the poll for Perry is that he isn’t breaking the 50-percent hurdle in those wanting to vote for him. Conventional wisdom has it that people know the incumbent for better and worse and there’s not usually a whole lot of movement — those who like him, like him, those who don’t are shopping for another candidate.