During a recent campaign swing, the answer was a resounding “si,” as the former Democratic National Committee chairman swept through Todos Supermarket in Woodbridge, Va., momentarily wielding a spatula behind the counter (“If the governor thing doesn’t work out, I can do this!”), vowing to pass a state-level DREAM Act, and repeatedly hailing the supermarket’s San Salvador-born owner, Carlos Castro, as an example of “the American dream.”

“We can’t grow our economy unless we ensure that Virginia is an open and welcoming state to everyone,” McAuliffe proclaimed, flanked by Democratic Del. Alfonso Lopez, the only Hispanic member of the state Legislature. “I’d love to see thousands of more Carloses by the end of my term as governor. We need to help the Carloses of the future grow and diversify this economy.”

( PHOTOS: Terry McAuliffe’s career)

The campaign stop was one of dozens that McAuliffe and his Republican opponent, state Attorney General Ken Cuccinelli, have made in an intense effort to court Virginia’s rapidly diversifying electorate. Indeed, take the event locations off the schedules of the two candidates and you might think they were running for mayor of New York — a feature of the campaign that’s likely to be replicated in more and more elections, as demographic change transforms the American political landscape.

Conventional wisdom states that in an off-cycle election, the voting population will be whiter and more conservative than it was during last year’s presidential race. But neither party’s nominee is acting like it, and with good reason.

Any McAuliffe win would almost certainly depend on turning out a greater-than-usual proportion of the “New Virginia” voters who handed the state twice to President Barack Obama. That may seem like a truism after Obama’s 2012 success here, but most Virginia Democrats have feared to even attempt this path to victory in the past. In 2009, the party hoped a rural state senator would win over enough conservative Virginians to put the governor’s race in play — and a few years before that, Democrat Jim Webb won an upset election to the U.S. Senate campaigning as a grizzled Scots-Irish veteran in the tradition of Andrew Jackson.

For Cuccinelli, on the other hand, making inroads with a more diverse electorate would be an important step toward leading the GOP to a statewide comeback in a battleground that hasn’t voted for a Republican senator or presidential candidate in nearly a decade.

( PHOTOS: Ken Cuccinelli’s career)

So far this year, the former state senator from Fairfax has attended meetings with the Pakistan American Business Association and the Moroccan American Network, celebrated Filipino-American culture at festivals in Richmond and Virginia Beach, courted the Vietnamese community in Falls Church and given interviews to Indian, Korean, Moroccan and Vietnamese-oriented media, among other outreach events.

McAuliffe’s focus on outreach has been, if anything, more relentless. He has toasted the Lunar New Year with Korean, Chinese and Vietnamese groups in Northern Virginia, celebrated the Persian New Year holiday of Nowruz, addressed a meeting of the Democratic Latino Organization of Virginia and held a special campaign kickoff aimed at the Asian-American and Pacific-Islander communities. He, too, has joined Filipino-American festivals and in July, he put up a “Ramadan Kareem!” message on Facebook to mark the Muslim holy month.

The political logic of these itineraries is straightforward: while Virginia has always had a sizable African-American population, the last 10 years have seen a sharp rise in other nonwhite voting groups. In the 2004 presidential race, Latino voters made up 3 percent of the Virginia electorate and Asians made up 2 percent, according to exit polls. By 2012, those numbers were 5 percent for Latinos and 3 percent for Asians — a combined 60 percent increase in those two heterogeneous groups. In a low-turnout election, that shift could be all the more consequential.

If the national GOP has been caught off-guard by the scale of change under way in the electorate, few Republicans are less surprised by this state’s transformation than Cuccinelli, who won multiple state Senate elections in a Fairfax-based district, near the epicenter of Virginia’s demographic change.

“I’ve been in the biggest melting pot in Virginia. It’s just been kind of something I’ve grown up with. It doesn’t strike me as all that unusual,” he told POLITICO after a meeting in Richmond with Asian-American business leaders in late July. “One of the things that frustrates me about the Republican Party is, you know, all the hand-wringing and everything else after 2012. ‘Oh, we’ve got to do this, we’ve got to do that.’ I’ve been doing it.”

Recalling the razor-thin reelection margin in his 2007 legislative race, Cuccinelli said: “I can just get around and meet a lot of leaders in those communities and listen to their advice … Without all that effort in the years before it, I probably would not have won that race.”

Cuccinelli’s outreach meeting in Richmond was a case study in both his strengths and limitations as an aspiring big-tent GOP leader, and the shadow the national conversation on immigration has cast over his campaign.

Speaking to a group of about 14 Asian-American Virginians, largely of South Asian descent, Cuccinelli emphasized his long ties to the state and his involvement in local institutions, contrasting that with McAuliffe’s upbringing in national politics. He said his top priority was making it easier for small businesses to create jobs — and while he’s no fan of “quotas,” Cuccinelli said internationally savvy constituencies should be better represented in the state’s overwhelmingly white economic development agencies and boards.

“He was able to discuss and articulate a specified plan … that’s actually going to help the majority of our community, the Asian-American community,” said Republican Tony Pham, an attorney for the Richmond sheriff’s office, who attended the event. “Any time there is a significant event that means a lot to the Asian-American community, the attorney general has made it a point to appear.”

Yet when one attendee asked Cuccinelli to answer for the national Republican Party’s “intolerant language,” Cuccinelli said only that he would “set the example” for others in the party once he’s governor. It was a response that left the questioner, Virginia Commonwealth University professor M. Imad Damaj, unsatisfied.

“He told us, ‘I’m going to be the role model for the Republican Party.’ That’s nice and I think the current governor did show that,” Damaj said, referring to incumbent Republican Bob McDonnell. “But that’s not tackling the bigger issues, talking to these communities about, ‘Do you feel that you are partners? Do you feel welcome in the state?’”

Damaj, who’s president of the Virginia Muslim Coalition, said he doesn’t question Cuccinelli’s personal interest in racial and ethnic inclusiveness. But Damaj got a clearer assurance from McAuliffe in a recent private conversation, paraphrasing McAuliffe as saying: “I don’t foresee myself governing this state without having all these communities represented.”

For his part, Cuccinelli says he has heard fewer concerns about the state of the national party recently than he did right after the 2012 election, “When people, not just people in politics, were chewing over what happened and why.”

“But it’s never completely gone and it’s a legitimate question,” he said. “It’s one of those things you’ve got to continuously look at. Are we presenting to everybody what we may have to offer for them?”

Still, it’s this big-picture, partisan and ideological fault line, that is the core of McAuliffe’s sales pitch to the Asian-American and Latino leaders he has wooed. Like Cuccinelli, he insistently broadcasts his commitment to helping small businesses. But where Cuccinelli seeks to distinguish himself from McAuliffe through his sustained engagement with Virginia communities, McAuliffe draws an equally sharp contrast around the more abstract concept of inclusion — the notion that he, and Democrats in general, are simply more comfortable with the new face of Virginia than their opponents are.

In the past few weeks, McAuliffe and Democratic campaign committees have attacked Cuccinelli for having once praised Iowa Rep. Steve King, the immigration hawk who recently warned of drug-smuggling illegal immigrants with “calves the size of cantaloupes.”

During his visit to Todos, McAuliffe told POLITICO that he hoped to draw sympathetic constituencies to the polls by highlighting the gulf in values that separates him and Cuccinelli.

“This is probably the starkest difference you’ve had between two candidates running for governor,” he said. “My opponent is on a social-ideological agenda. In my bones, you cannot grow an economy and diversify it when you have these hate-filled statements — as it relates to women’s health centers, gay Virginians, the issues on immigration we’ve seen in the last couple days. I want to stop all that.”

Lopez, the state lawmaker who toured the supermarket with McAuliffe, said this election could be a watershed moment for Latinos in Virginia, who have “been systematically demonized by Republicans in Virginia for 11 years, with legislation, with ads.”

“The demographic shifts in the Commonwealth of Virginia, if they continue to move in the way they’ve been going, I think you’re going to see us become more solidly purple and increasingly light blue,” said Lopez, who led the charge for a Virginia DREAM Act over the past year.

With the election still three months away, it’s still unclear exactly what kind of electorate will show up to vote. And as much as both candidates are doing their best to win over a highly multicultural electorate, neither will be shocked if many Obama voters — not just nonwhite Virginians, but also young people — stay home. That’s what happened in the last governor’s race: after white voters made up 70 percent of the Virginia electorate in 2008, that number jumped to 78 percent in the 2009 governor’s race that McDonnell won handily.

Herndon town council member Grace Han Wolf, a McAuliffe supporter who was the first Korean-American woman elected to office in Virginia, said that her own ethnic community — and many others — still have work to do as far as engaging in state politics.

“The last two presidential cycles kind of did energize the entire ethnic community, because there was a bit more reason to get involved. The good thing is, they remain more sensitized to the entire electoral process,” she said. “But it’s still a glacial pace. Neither of the candidates is particularly well-known. I know in the Korean-American community, it’s like, ‘Oh, it’s two white guys.’”

Han Wolf noted that some of the topics regarded as wedge issues overall in the race — abortion and gay rights, for example — aren’t especially effective subjects in the Asian-American community. The same could be said for at least some other culturally traditional, but Democratic-leaning groups.

“You have to approach this community with messaging that’s relevant to our constituencies,” she said. “I think you’re seeing since the Obama election an understanding that the Latino vote is going to have a little bit of a different perspective than the [Asian-American Pacific-Islander] vote, or the black vote, or the Muslim vote.”

Moroccan American Network President Mohamed El Hajjam, who has met both gubernatorial nominees and whose group hosted Cuccinelli earlier this year, said the level of attention from major political candidates these days is unprecedented – and welcome.

“I’ve lived here almost 18 years and seen a lot of changes in the landscape,” he said. “We’re happy to see more of them up close, which we’re not accustomed to.”