When Sen. Marco Rubio joins Ken Cuccinelli II at a Richmond fundraiser Monday, the duo together will embody the two sides of one of the GOP’s chief challenges — immigration reform — as the party tries to win back purple states where Barack Obama stitched together a coalition of minorities and women in back-to-back national elections.

Rubio is one in a succession of GOP stars coming to Virginia to help Cuccinelli energize his campaign for governor against Democrat Terry McAuliffe. But Rubio’s visit does something else, too: It brings attention to the polar-opposite ways in which the two Republicans have struggled over the question of what do to about the estimated 11 million people in the country illegally.

Rubio (R-Fla.) helped author a comprehensive Senate plan that includes provisions to give undocumented immigrants a chance at citizenship, a high-risk effort that polls indicate has eroded his support among the GOP base.

Cuccinelli, Virginia’s attorney general, championed hard-line immigration policies while rising through the state ranks — but he has awkwardly sought to play down his record in hopes of not alienating Hispanics and Asians who represent a small but growing part of Virginia’s electorate.

Republican leaders have conceded that presidential nominee Mitt Romney damaged his candidacy last fall by promoting “self-deportation,” and some have pushed the party to embrace more liberal policies to woo Hispanics and move the issue off the agenda in future elections.

Cuccinelli isn’t quite doing that, but his appearance with Rubio at the tickets-only fundraiser suggests that he is trying to soften perceptions about his stand on immigration.

It’s been a notable shift for a candidate who vocally opposed President George W. Bush’s 2007 push for immigration reform. Asked recently by reporters whether he supports the Senate bill, Cuccinelli replied that he had not read the legislation and specified only that he does not support amnesty for undocumented immigrants.

“I sure as heck would like to see them resolve this issue in some way in Washington,” he said during a campaign stop in Ashburn. “I’m running for governor. That is a state office.”

Immigration advocates said Cuccinelli, who scrubbed a section on immigration from his campaign Web site in the spring, is not fooling anyone with his vague answers. As a state senator, he sponsored legislation aimed at stripping U.S.-born children of illegal immigrants of their right to citizenship, and as attorney general he has embraced policies that would authorize police to check the immigration status of anyone they stop or arrest.

Cuccinelli also has been accused by Democrats of comparing immigration policy to pest control.

Danny Vargas, an influential Republican businessman from Herndon, said he would like to see Cuccinelli’s views evolve on issues such as state legislation to grant some government benefits, such as in-state tuition to college, to undocumented immigrants brought to the country at a young age by their parents.

Democratic rival Terry McAuliffe supports such legislation, but Cuccinelli voted against similar proposals in 2008 and 2009.

“I don’t doubt that he and others may have taken a harder line on it, but that’s a lot of water under the bridge from 2007 to today,” Vargas said. “The country has come to grips with having to come up with a national solution on immigration reform. Now that we’ve had a general election [in 2012], as opposed to just a Republican primary, folks on the left, right and center are all about finding a solution.”

A June survey by the Republican firm Harper Polling found that 86 percent of Virginians believed it was important to fix the immigration system this year, and 69 percent supported a path to citizenship for immigrants who paid fees and taxes and learned English over an extended period.

But as Rubio discovered, moving to the middle risks a backlash from the far right: His favorability rating fell 15 points from February to June as he championed immigration reform. Sens. Ted Cruz (R-Tex.) and Rand Paul (R-Ky.), two other tea party favorites with an eye on 2016 White House bids, voted against the Senate plan, and House Republicans have refused to vote on it.

Cuccinelli’s spokeswoman said campaign events are being planned with Cruz and Paul.

Former congressman Tom Davis, a Republican from Northern Virginia, said Cuccinelli has made it clear that he will not risk offending his base — on immigration and also on gay rights and contraception — in hopes of knitting together a broader coalition that would include more moderates.

“It’s hard to win a statewide election with that,” Davis said. “I told him he needs to be more inclusive. People moving into the state are not in agreement with the party they’re constructing.”

Other Republican strategists argued that Cuccinelli is not trying to play both sides of the issue. Rather, they said, he has de-emphasized his immigration positions in a campaign that has focused primarily on jobs and the economy. Cuccinelli and McAuliffe have also spent considerable time deflecting questions about personal business relationships.

Former GOP state representative Jeff Frederick of Prince William County suggested that Cuccinelli erased the immigration portion of his Web site because it’s “not what people are thinking about when he goes to meet with voters.” The site includes sections on education, energy, jobs, veterans, moms and students.

Hispanics are still a small bloc in Virginia: They made up 5 percent of the state’s electorate last fall, with Obama winning 64 percent of their votes.

Ray Allen, a GOP political consultant in Virginia, said that “neither campaign has been articulating an agenda around immigration.” While Virginia once was a leading battleground over illegal immigration — from the Sept. 11, 2001, terror attacks, in which several of the hijackers had ties to Virginia and Virginia driver’s licenses, to the fight over day laborers in Prince William County — the issue is now primarily a federal one, Allen said.

“Is this a question that’s relevant to the governor’s race? No,” Allen said. “I could give you 10 issues that McAuliffe’s taken positions on [as a Democratic Party leader] that he’s not bringing up this election.”

But immigration could gain more prominence in the race. The candidates are scheduled to appear at an Oct. 6 forum in Annandale sponsored by Virginia’s Hispanic, Asian and black chambers of commerce, and the issue will be among the featured topics.

“We want to know where he stands,” Hispanic Chamber President Michel Zajur said of Cuccinelli. “It’s something that hurt Mitt Romney when he was running. . . . It very well may have cost him the election.”