Evan McMorris-Santoro June 18, 2010, 9:53 AM

A new Rasmussen poll shows Texas Democratic gubernatorial nominee Bill White is running close to incumbent Gov. Rick Perry (R).

The poll, taken on Wednesday among 500 likely voters, shows Perry in the lead by a margin of 48-40. The poll has a margin of error of 4.5%.

Past polling has shown Perry with a wider lead. In the last Rasmussen poll, taken on May 13, Perry led 51-38.

The TPM Poll Average for the contest shows Perry ahead by a margin of 49.0-39.1.

National Democrats have been suggesting that White could pull off what would be seen as an upset win in Texas for a while now. The popular former mayor of Houston and a former Clinton Administration Energy Department official, White swept a field of Democratic candidates to win his party’s nomination in March.

Since then, White has been on the attack — accusing Perry of being “a part-time governor” after releasing public schedules to the media showing Perry “worked about seven hours a week” from January 1 through the primary, according to the AP and sending a man in a chicken suit to Perry events taunting the incumbent for refusing to debate White.

Perry has had his own problems to deal with beyond the campaign. He’s under fire for the lavish temporary residence taxpayers are paying the rent for while the Texas Governor’s Mansion in Austin is under repair. He’s also facing an insurgency within his own party over the Arizona immigration law — Perry’s opposed to it, but the state GOP voted in favor of imposing legislation just like it in Texas at their state convention last week.

But Perry has proven himself to be an able campaigner, winning a three-way primary that included Sen. Kay Bailey Hutchison to win the right to run for a third term as the Republican nominee.

Bill White, Rick Perry, TX-GOV