LAS VEGAS – In recent months, Sheriff Joe Arpaio has tried to extend his political reach outside his home state of Arizona, where he’d gained national notoriety for lightning-rod tactics to root out illegal immigrants.

With Arizona’s controversial immigration law, rekindling national interest in border security, Arpaio has appeared in Kentucky and Kansas and elsewhere as an emblem of a stern law-and-order approach. Today, he’s scheduled to speak at a GOP lunch in the key primary state of New Hampshire, which has led some observers to wonder if he’s mulling a presidential bid.

Last week Arpaio waded into the high-profile Nevada Senate race, cheering on Republican Sharron Angle, a tea party favorite locked in a tight contest with Senate Majority Leader Harry Reid.

It may provide a test of how voters outside Arizona view Arpaio, who fancies himself “America’s toughest sheriff” and was sued this month by the Justice Department, which accused him of refusing to cooperate with a federal civil rights probe.

“He represents being tough on crime and tough on immigration, and I can see a lot of politicians wanting his endorsement,” said Kenneth Fernandez, an assistant professor of political science at the University of Nevada, Las Vegas.

Arpaio has recently been touting the power of his support, saying it carried more weight than that of Republican Sen. John McCain, at least in Arizona. Arpaio, sheriff of Pima County, which includes Phoenix, won re-election in 2008 with 55 percent of the vote.

Arpaio has been testing his political strength outside the Grand Canyon State by supporting candidates for Michigan governor, California Assembly and congressional seats in Florida and Missouri, among others. His political adviser, Chad Willems, said a number of GOP candidates have sought the sheriff’s backing, though his track record out of state has been less successful than in Arizona.

“He likes to spot underdogs and help those not necessarily part of the establishment. He doesn’t always pick the winner,” Willems said. The sheriff did not reply to a request for comment.

His endorsement of Steve Poizner made little difference in California’s GOP gubernatorial primary — Meg Whitman won — his backing has been highly coveted in strongly GOP legislative districts, said Allan Hoffenblum, publisher of the nonpartisan California Target Book.

“He’s too hot for a statewide candidate,” said Hoffenblum, a former GOP consultant. “To win statewide in California you need a large Latino vote, and you’re not going to get a large Latino vote if you showcase him.”

Reid and Angle, as with many issues, hold polar-opposite immigration views. Though in 1993 Reid supported a bill that would have denied citizenship to children of undocumented immigrants, he later called it the “biggest mistake I ever made.”

Last week after Arpaio said he’d support Angle, Reid’s team mocked his statement as a ” ‘sure, who cares?’ nod” from an outsider. “Sen. Reid is proud to have the overwhelming endorsement of law enforcement right here in Nevada,” said Reid spokesman Kelly Steele.

Immigration could be a tricky issue for Reid. Arizona’s tough law, much of which was put on hold by a federal judge, has the backing of a majority of Nevada voters, according to polling for the Las Vegas Review-Journal and KLAS-TV.

Angle spokesman Jarrod Agen sums up Reid and immigration this way: “Sheriff Joe’s support helps tremendously because it highlights an issue in which Harry Reid stands against the mainstream majority of Nevadans.”