LAS VEGAS — Organized labor’s divided loyalties between Hillary Rodham Clinton and Bernie Sanders coursed through the Luxor hotel and casino here this week, where both Democratic presidential contenders courted voters at a statewide convention of the Nevada AFL-CIO.

Clinton, who addressed the gathering late Tuesday, has deep connections to labor. She received significant endorsements during her unsuccessful run against Barack Obama in 2008. But her equivocations on issues such as the looming Trans-Pacific Partnership and whether to raise the federal minimum wage to $15 have given some union members pause this time around.

Sanders, a senator from Vermont, has drawn huge crowds with sizable union representation and his poll numbers have risen in recent weeks as he touts many of the same positions that labor champions. But even boosters question whether a self-described democratic socialist can win a national election.

Although labor unions’ strength has waned in recent years, they remain a force in general-election campaigns in battleground states such as Ohio, Pennsylvania and Wisconsin.

And the politics of labor endorsements have grown more sophisticated. Several labor organizers suggested that the AFL-CIO and its member organizations have an incentive to hold off on endorsements because doing so gives them more leverage to get the candidate they endorse to buy into their ideas.

But other unions have seen an opportunity to make a point with early endorsements.

National Nurses United, which represents 185,000 nurses across the country, last week became the first national union to endorse Sanders. Among other things, the organization cited Sanders’s support for a single-payer “Medicare for All” health-care system, a liberal idea that Clinton has not embraced.

RoseAnn DeMoro, executive director of the nurses union, said that Clinton — a former first lady, senator and secretary of state — has long been considered the “coronation candidate” of the Democratic establishment and that she received many thank-yous from other unions for having the courage to step out in Sanders’s direction and “fight for something.”

Yet even DeMoro acknowledged Sanders’s principal challenge, saying, “The real debate going on in the background is about Bernie Sanders’s viability.”

The nurses union’s endorsement came in the wake of a decision by the national AFL-CIO, labor’s umbrella group, to delay a primary endorsement after its executive council met in Silver Spring, Md., with Clinton, Sanders and other candidates in July. The Sanders camp touted the non-decision as a victory, but Clinton supporters are quick to point out that the organization has thrown its weight behind a candidate during contested primaries only twice before: Walter Mondale in 1984 and Al Gore in 2000.

The lack of an AFL-CIO endorsement has sparked more intense battles for nods from its 56 member organizations, two of which are supporting Clinton: the 1.6 million-member American Federation of Teachers and the 600,000-member International Association of Machinists and Aerospace Workers.

Randi Weingarten, president of the AFT, said Clinton is strong on her union’s issues, including expanding early childhood education, supporting the teaching profession and reducing college debt. But part of the calculation, she said, is who would be in a position to prevail against the Republican nominee next year in an election when monied interests aligned with the GOP are expected to spend so heavily.

“In national politics these days, you have to not simply have great ideas, but you have to have the infrastructure and ability to get elected,” Weingarten said.

When Sanders met with the AFL-CIO’s executive council last month, he produced polls showing how strongly he might fare against various Republican nominees.

Weingarten said that even if the AFL-CIO doesn’t endorse a candidate during the primaries, she expects “a lot of enthusiasm” for Clinton because of the high stakes for working families and the hostility toward unions that many of the Republican candidates have shown.

Here in Nevada, the most powerful union, the 55,000-member Culinary Workers Union Local 226, is in no hurry to endorse before it hears where candidates stand on its most important issue at the moment: repealing the “Cadillac tax” in President Obama’s health-care law.

At issue is a 40 percent tax on expensive insurance plans, scheduled to take effect in 2018, that’s meant to slow the growth in health-care spending while raising revenue.

“Once we fix Obamacare, we can look at other issues,” said Yvanna Cancela, political director of the union, which represents casino and hospitality workers and is affiliated with the Unite Here union. The majority of the culinary workers are Latino, and immigration issues have been at the fore in the past.

Speaking to reporters here after his closed-press remarks to the AFL-CIO, Sanders said he supports the effort to eliminate the excise tax on health benefits earned by union members in collective bargaining agreements. During her speech, Clinton pointed to signs held by activists saying “Fix Obamacare” and said she is looking at the issue.

Former Maryland governor Martin O’Malley, another Democratic hopeful considered strong on labor issues, is scheduled to address the convention Wednesday.

According to some of the 200 labor activists in the room Tuesday, both Sanders and Clinton were warmly received, with many people crowding them for photos afterward.

The culinary union endorsed Obama over Clinton in 2008 in what became a rough-and-tumble caucus process. A dispute over whether voting should take place in casinos led to a Spanish-language radio ad accusing Clinton of trying to keep people from participating. Clinton wound up winning the popular vote in the caucuses, but Obama emerged with more delegates from the state.

Cancela said the union is keeping an open mind about Clinton this time.

“I think our membership, like the rest of the country, is listening and learning and getting to know her as candidate in 2015 as opposed to 2008,” she said.

While in Nevada on Tuesday, Clinton also visited the sprawling new training center for the United Brotherhood of Carpenters, another union that could be on the verge of delivering an early endorsement. Carpenters President Doug McCarron introduced Clinton as “the next president of the United States” to big applause from a crowd of about 50 assembled carpenters.

R. Thomas Buffenbarger, president of the machinists union, which endorsed Clinton late last week, defended her for her less-than-definitive stance on the Trans-Pacific Partnership, which Sanders and O’Malley have spoken out against.

Obama has touted the proposed 12-nation trade and regulatory deal as a cornerstone of his second-term agenda, but opponents say the chief beneficiary will be large multinational corporations.

During a private meeting with his union, Buffenbarger said Clinton explained that she, like most Americans, hadn’t seen the deal and “can’t come out as clearly on TPP as some people might want her to.” He said that struck him as a reasonable position.

Rand Wilson, a Sanders supporter who is helping lead a group called Labor for Bernie, predicted several unions will slow their endorsement process, given the popularity of Sanders among their rank-and-file members. More than 6,500 people have signed a letter on the group’s Web site endorsing Sanders.

“They’re not used to seeing this kind of enthusiasm from the grass roots,” Wilson said of labor leaders. “It’s given them a reason to take some time to get in touch.”

Robert Gilmore, secretary-treasurer of the International Union of Painters and Allied Trades district council in Iowa, said Sanders’s electability in a general election is not an issue for him.

“It doesn’t scare me,” Gilmore said. “If the country’s not afraid of Donald Trump, I don’t know why they should be afraid of Bernie Sanders.”