Barack Obama, meet Adriana Lima. Adriana, Barack. Barack, Adriana.

Lima is a 21-year-old Brooklyn native majoring in journalism at Baruch College in New York. She is Latina. She’s a registered Democrat--and no relation to the Brazilian supermodel of the same name. Next November Lima will cast her first vote for president. She might vote in the New York Democratic primary on Feb. 5, too.

Barack Obama really wants Lima’s vote. In fact, he wants it--and the votes of her 18- to 29-year-old peers--so badly that on Thursday evening, after enduring New York’s arduous permit process and dispatching volunteers with tickets to Lima’s college (and other campuses in New York), Obama closed off Washington Square Park, 9.75 greenish acres at the heart of Greenwich Village and New York University, and welcomed dozens of Secret Service agents, scores of cops, four giant metal detectors, a herd of police dogs and, ultimately, 24,000 supporters, curious locals, ’60s holdovers, dog walkers, yoga devotees and punk rockers--the vast majority of them only a few years younger or older than Lima--to his first Big Apple rally (and largest event to date). “This year young voters are the most energized part of the electorate,” says deputy campaign manager Steve Hildebrand, who’s running Obama’s ground game in the early states. “We’re confident that they’ll be a crucial part of Barack’s percentage take in Iowa on caucus night and primary day in New Hampshire, and so on.”

The campaign is fond of reciting poll results and Facebook stats as proof of its appeal to Generations X and Y. But most young voters are less like the 362,000 who have joined Facebook’s “One Million Strong for Barack” group and more like Lima, who arrived at Washington Square Park around 4:30 with “no idea” which candidate she would support for president. She came, she said, “on a fluke.”

With Obama not scheduled to take the stage until 7:00, the campaign spent the next few hours buttering up the kids. Spicy Spanish guitar renditions of “Stairway to Heaven” and Shakira’s “Hips Don’t Lie” blared over the PA. Indie rockers the Northern sang sensitive acoustic songs with lines like “You are everything to me / Like salt is to the sea” and told the crowd to “check us out on MySpace.” Obama’s national field director, Temo Figueroa, admitted that he’d “brought [his] posse with [him],” because “that’s the way you roll in New York.” (It is also, coincidentally, “the way you roll with the Obama campaign,” according to Figueroa.) Actor Geoffrey Wright (“Syriana”) recalled “the smoke and haze” of his first Independence Day in New York, “when the city was a freer place.” And after encouraging the audience to “make some noise,” hip-hop recording artist Jin began rapping about the senator’s virtues (“Gas prices are outlandish / He says we need higher fuel-efficiency standards”) and requesting that “When I say O, you say Bama.” Around 6:30 Lima looked at her watch. “If I knew I had to put up with all of this,” she said, “I wouldn’t have come.” But doesn’t Obama have to appeal to young voters? I asked. “It’s not working,” she said.

As is so often the case, though, the main act outshone the openers. Speaking through the cold that had vexed him at the previous night’s New Hampshire debate, Obama was clear and forceful. With a few exceptions--a shout-out to “the bars around here”; a confession that, despite Hillary Clinton’s recent hemming and hawing, he would pick the White Sox over the Yankees any day--the senator did not pander to the youthful crowd. Instead he stuck to his usual message of “hope”--if at times drawing sharper distinctions than usual between himself and his colleague from New York. “There were folks on the [New Hampshire debate] stage that said Social Security is just fine; we don’t have to do anything about it,” he said, referring to Clinton. “There are folks who will shift positions and policies on all kinds of things depending on which way the wind is blowing. That’s not the kind of politics that will deliver on the change we are looking for.”

The change Obama is looking for, as he frequently notes, is generational--a shift from the “division and deadlock” of the Baby Boomer era to a “new politics” of “decency and generosity.” The theme appealed to Thursday’s savvy, cosmopolitan rallygoers, who nodded and smiled when Obama said, “There are easier choices to make in this election: competent people who will manage the system as it is,” and cheered when he asked, “Are you willing to take a risk?” But it’s still unclear whether all his talk of process--as opposed to actual kitchen-table concerns--is enough to win over the rest of the Democratic electorate, which still prefers Clinton by more than 17 points in national polls.

It wasn’t enough, it seems, to win over Lima. “He was better than I thought he’d be,” she said as Obama left the stage. “But I don’t know. It’s still too early to say.” And then off she went with the rest of the twentysomethings, Yellowcard’s emo hit “Believe” echoing across the park.