The new numbers have Perry at 48 percent to White's 40 percent. Meanwhile, 5 percent are going for some other candidate and 8 percent are "not sure."
This is tighter than Rasmussen's previous poll, which showed Perry leading White 51 percent to 38 percent.
Of all Texas voters, 53 percent approve of Perry's job performance as governor, while 45 percent disapprove.
The pollsters also found that 15 percent of Texas voters view Perry very favorably, as opposed to 21 percent who view him very unfavorably. Those stats for White are 18 percent and 16 percent, respectively.
Other notable findings:
Texas voters have consistently voiced even stronger opposition to the national health care bill than is found among voters nationwide. Sixty-five percent (65%) of voters in the state favor repeal of the health care bill, while 32% oppose repeal. This includes 58% who Strongly Favor repeal of the bill and 21% who are Strongly Opposed.
Texas voters tend to have an unfavorable opinion of Supreme Court nominee Elena Kagan and to oppose her confirmation by the Senate. But like voters in much of the rest of the country, a sizable number aren’t sure whether she should be confirmed or not.
Forty percent (40%) of Texas voters approve of the job President Obama is doing, but 60% disapprove. This is higher disapproval than is found nationally in the Rasmussen Reports daily Presidential Tracking Poll.