SPECIAL REPORT-Is immigration a desert mirage for the G.O.P.?

* Five states to follow Arizona; 20 more may do so soon

* Obama legal challenge energizes anti-big government set

* But damage to Democrats in House races appears limited

* Republicans risk alienating key Hispanic support in 2012

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By Tim Gaynor and David Schwartz

PHOENIX, July 27 (Reuters) - Republican state Senator Russell Pearce, a long-time fixture in Arizona politics but until recently a virtual unknown elsewhere, never expected to singlehandedly shake up national politics, let alone get under the skin of the White House.

"Nobody could have guessed the impact it would have," Pearce said of the divisive law he crafted to crack down on illegal immigrants in his state -- of which there are nearly half a million. "Who could have guessed that I would have pissed off the president of the United States?"

A 63-year-old father of five and former lawman who worked for the local Maricopa County Sheriff's Office for 23 years, Pearce is clearly reveling in the political shockwaves he has created. He says he is also pleased to have called attention to what he and many other Americans consider misguidedly lenient policies toward illegal immigrants.

As a result, Arizona -- the desert state that provided presidential candidates in Barry Goldwater and John McCain -- has become a crucible for policy on immigration, an issue that crystallizes popular anger ahead of the midterm congressional vote in November.

The state's controversial law goes into effect on Thursday, barring successful legal challenges. It will make it a crime to be in the country without proper documents. Local backers say the legislation's intent is to curb the smuggling of both humans and drugs over the state's porous border with Mexico.

It also requires state and local police officers to check the immigration status of anyone they suspect is unlawfully in the country, even during routine traffic stops. Critics say that this will inevitably result in widespread harassment of Hispanic or Hispanic-looking Americans.

Even so, polls show the Arizona approach is supported by a solid majority of Americans -- a Rasmussen Reports poll in late May found 55 percent of respondents nationally would like a similar law in their own state. Consequently, some political experts say President Barack Obama's steadfast opposition to it will likely help galvanize grass-roots Republican groups.

More significantly, the new law appears to be inspiring copycat efforts in at least 20 other states. That is in addition to the five states that have already introduced similar legislation this year.

As wedge issues go, however, this one may well end up languishing in the desert. Many political analysts say illegal immigration is unlikely to be a deciding factor in all but a handful of contests -- mostly in Arizona itself.

And the eventual backlash against the measure, experts say, could prove severe for its champions, alienating an increasingly affluent Hispanic electorate once considered a potential conservative goldmine for the Republican Party.