Two weeks from now, North Carolina will hold a public referendum on what could become one of the toughest anti-gay measures in the country: a far-reaching proposal to amend the state constitution to ban civil unions and domestic partnerships. But President Obama did not touch the subject when he appeared in Chapel Hill on Tuesday — even though it is roiling the electorate there.

Instead, Obama talked about college loans, kicking off a two-day, three-state tour designed to energize the youth vote. His delicate sidestep of Amendment One, a ballot initiative to be decided May 8 that would recognize marriage between a man and a woman as the only legal domestic partnership in North Carolina, is seen by some as another sign that he is not fully committed to gay rights — an interpretation that could dampen the enthusiasm of the young voters he is trying to court.

“It’s a little bit of a missed opportunity,” said Josh Orol, 20, a sophomore at the University of North Carolina at Chapel Hill and a leader of a campus movement to defeat Amendment One. “I didn’t expect him to talk at length about it. I know he has come out publicly against it. But I sort of hoped he would at least name-drop a little bit. It’s disappointing.”

The issue is particularly complicated in historically conservative North Carolina. Obama scraped together a razor-thin victory there four years ago with a multicultural coalition that included independents, African Americans and Hispanics — constituencies that are less uniformly enthusiastic about expanding gay rights than campus activists.

North Carolina is widely seen as a bigger challenge this year for Obama than it was in 2008, when he won with a margin of roughly 14,000 votes. Not only does the state’s unemployment rate continue to hover near 10 percent, but its Democratic Party is in disarray and is expected to be of little help to president: The Democratic governor, Beverly Perdue, is not popular and decided not seek reelection this year. The trial of embattled one-time presidential contender John Edwards began this week. And the state party organization is being rocked by a scandal, with its executive director forced out over sexual-harassment allegations.

None of these challenges have stopped Obama from planting a flag in North Carolina, as he did by deciding to hold his party’s national convention in Charlotte this year. His campaign has opened more than a dozen offices around the state. In fact, Obama’s grass-roots organization never really dismantled four years ago — and actually as grown since then, state campaign officials said.

“The truth is, the real organization down here, the real powerhouse organization, is the Obama organization,” said Democratic operative Gary Pearce, a longtime aide for former governor Jim Hunt. “It was always expected that it was going to be up to the Obama campaign to take the lead here.”

It will also be up to Obama to navigate the political crosscurrents of a complicated state in which he must court multiple constituencies that do not all agree on all the same issues.

The fate of Amendment One, for instance, is uncertain, with one public poll predicting that it will pass easily and another projecting a loss. Quietly opposing Amendment One, but keeping his distance from on-the-ground efforts to defeat it, could be an essential strategy for Obama to pull back together the diverse coalition that elected him last time.

Nonetheless, that approach is frustrating younger activists, many of whom have come to view marriage equality as the defining civil rights cause of their generation. They are impatient with Obama’s self-described “evolving” position on gay marriage — he supports civil unions but stops short of endorsing legal protections for marriage — and they are looking for signs that he is ready to embrace their cause more fully.

“The ‘evolving’ position does frustrate people, especially young people, because it’s such a no-brainer to us,” said Jeff DeLuca, 21, a senior at UNC-Chapel Hill and another organizer against Amendment One. “When it’s all said and done, young people are going to vote this down 70-30. There is just a very strong generation gap.”

Campaign and White House advisers emphasized Obama’s official opposition to Amendment One — the campaign announced his objections to it last month — and noted that it would be unusual for a president to mention a ballot initiative at an official event such as the one in Chapel Hill on Tuesday.

Campaign officials also drew a stark contrast between Obama’s positions on marriage issues and those of the presumptive Republican nominee, Mitt Romney, whose opposition to legal protections for gay couples drew an endorsement last week from the National Organization for Marriage.

“The president has done more to advance gay rights than any other,” said campaign spokeswoman Clo Ewing. “From keeping his word to repeal ‘Don’t Ask, Don’t Tell’ to granting hospital visitation rights to gay partners, this president has a record of support.”

Particularly frustrating to DeLuca and others is the prospect of Amendment One passing despite growing opposition. Corporate leaders, advocates for victims of domestic violence and even moderate Republicans, faith leaders and the NAACP have joined forces in an attempt to defeat it because of concerns that it would block domestic benefits and domestic-violence protections not only for gay couples but also for heterosexuals who are not married — and their children.

If Amendment One passes, these opponents say, it will be because most North Carolinians did not understand its breadth. Obama has an opportunity to educate the public in a way that would sway voter opinion — even among the groups that usually lean toward traditional marriage, these advocates say.

The advocates are also hungrily eying the president’s formidable grass-roots operation, which they would love to tap into to defeat Amendment One.

“We certainly think that this would be a great opportunity for them as a dry run for November,” said Stuart Campbell, executive director of Equality North Carolina, a gay rights group. “But that’s really a decision for them to make, and as far as I know they have not made that decision.”

Whatever Obama does or does not say about Amendment One in the coming two weeks, he could benefit, at least somewhat, from the push to defeat it. Across the state, particularly on college campuses, diverse coalitions of students, gay rights activists, libertarians and others have been collecting e-mail addresses and registering voters in advance of the May 8 referendum.

Many of the activists turned out for an organizational meeting on campus last week at which volunteers were being sought for Obama’s appearance Tuesday. It took less than an hour for organizers to sign up 150 volunteers.

They may want more love from Obama on Amendment One, but they are still planning to support him in November.

“I’m going to vote for the president,” said UNC student Peter Vogel, 18, an anti-Amendment One organizer. “I’m not a single-issue voter by any means, but it would make me very pleased if he said something about Amendment One Tuesday. He’s in a tricky position.”