Controversial Arizona Sheriff Is Strongest GOP Candidate for Governor

Republicans had welcomed Brewer's ascension to the job after President Obama had chosen her predecessor, Democrat Janet Napolitano, to be secretary of Homeland Security. But Brewer, a staunch fiscal conservative, got into a bitter fight with Republicans in the state legislature over her push for a sales tax increase to plug holes in the budget. Fifty-seven percent of voters disapprove of her job performance, while 39 percent approve, with 5 percent undecided, Rasmussen says.

Attorney General Terry Goddard, expected to be the Democratic candidate, leads Brewer by 44 percent to 35 percent, with 9 percent preferring some other candidate and 12 percent undecided.

But Arpaio, a fierce foe of illegal immigration who calls himself ''the toughest sheriff in America,'' leads Goddard 51 percent to 39 percent, with 7 percent preferring someone else and 4 percent undecided.

Arpaio is best known for his aggressive sweeps of Hispanic neighborhoods, making use of a federal program that allows state and local police officers to enforce U.S. immigration laws. But officials of the Immigration and Customs Enforcement agency withdrew authorization to do so from Arpaio's department.

Arpaio countered that he could continue to pursue illegal immigrants under state law, and the Rasmussen poll said voters, by 64 percent to 29 percent, favored Arpaio in that effort.

A third Republican, State Treasurer Dean Martin, trails Goddard 40 percent to 38 percent, with 11 percent preferring someone else and 11 percent undecided. The margin of error is 3 percent.