LAS VEGAS (Reuters) - Democratic presidential contender Elizabeth Warren defended her Medicare for All healthcare proposal on Monday, telling members of an influential Nevada labor union that she wants all Americans to have coverage that is as good as theirs.

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Union members throughout the U.S. are worried about losing hard-won health coverage under plans by Massachusetts Senator Warren, and rival Vermont Senator Bernie Sanders, who have proposed doing away with private insurance.

Asked whether she would preserve the coverage negotiated by Nevada’s unionized hotel and casino workers, Warren pivoted, praising their state-of-the-art clinic but not saying how she would protect it.

“What you’ve got is something I want to see replicated all across America,” said Warren told a member of Culinary Workers Local 226 at a town hall meeting sponsored by the union Monday night in Las Vegas.

Warren was the first of three leading candidates seeking the Democratic Party’s nomination to run against Republican President Donald Trump in 2020 to appear this week at town halls hosted by the 60,000-member local.

Her participation, to be followed by Sanders on Tuesday and former Vice President Joe Biden on Wednesday, shows the significance of labor’s support to candidates vying for the party’s nomination just two months before the early-voting state of Nevada picks its choice.

Unions are so crucial to Democrats’ electoral success in Nevada that early voting for the state’s February nominating caucuses will take place in union halls.

All three of the candidates are allied with labor, but touchy questions remain for Warren and Sanders on their healthcare proposals. Both have said their plans would lead to the elimination of private healthcare, although Warren just days before her last trip to Nevada made a point of saying healthcare clinics funded under union contracts would be allowed to continue to operate under her plan.

Like many unions, the Culinary Workers have not yet endorsed a candidate among the 15 still vying for the party’s nomination, and healthcare will be key to its choice, said Geoconda Arguello-Kline, the 60,000 member local’s Secretary-Treasurer.

“One of the reasons they’re in a union is that it provides them with healthcare,” said Donna West, Democratic Party chairwoman in Clark County, where Las Vegas is located.

Biden, who is leading in polls in Nevada and nationally, has promised to preserve union healthcare as part of any reform.

But Biden, who served as Obama’s vice president, may face tough questions on immigration stemming from that administration’s high deportation numbers.

Culinary Workers, the state’s largest union, is heavily comprised of immigrants who work in casinos, hotels and bars.