Mayor Annise Parker polled 40 percent against Gov. Rick Perry’s 47 percent in a Public Policy Polling poll

Public Policy Polling’s latest indicates that Texans are ready for a change in the governor’s office. The polling outfit looked at everyone from one of the LGBT community’s staunchest opponents to a member of the LGBT community.

Of Republican Primary voters, 41 percent want Gov. Rick Perry to run for another term while 47 percent want someone else. Among Texans in general, 31 percent favor another Perry term while 61 percent don’t.

Attorney General Greg Abbott is the governor’s closest opponent and trails Perry by just 3 points. But Abbott doesn’t have good name recognition. Among voters who know him, he leads 55 to 33 percent. (Abbott is perhaps best know in the LGBT community for challenging two same-sex divorces.)

The poll shows that Democrats have a better chance to taking the governor’s mansion if Perry wins the Republican Primary.

Against three Democrats, Perry would get 47 percent of the vote, according to PPP. San Antonio Mayor Julian Castro polls 42 percent, State Sen. Wendy Davis would get 41 percent and Houston Mayor Annise Parker would get 40 percent.

Castro was a strong supporter of nondiscrimination in San Antonio. Davis ran for re-election last year with support from Equality Texas and Stonewall Democrats of Tarrant County. Parker, who is lesbian, is in her second term as mayor, making Houston the largest city with an LGBT person at the helm.

None of the Democrats has indicated whether they have interest in running for governor yet. Abbott has told supporters he plans to run.

The general election will be in November 2014.