Ms. Warren has attempted to allay voters’ reservations on that front in recent weeks by pledging not to raise middle-class taxes to pay for her plans. She also described how she would prioritize improvements to the Affordable Care Act, including the creation of an optional government health-insurance plan, before attempting to create a single-payer system.

Both Ms. Warren and Mr. Sanders remain among the best-positioned candidates in the primary election, with distinctive appeal to young people and other voters seeking a large-scale redraw of the political system — an overlapping agenda that drew roars of approval at the “First in the West” dinner.

At the dinner, both expressed disdain for incremental politics, with Mr. Sanders saying that “tinkering around the edges just won’t do what needs to be done” and Ms. Warren dismissing more modest policies as “a nibble here and a nibble there.” Both are polling at or near the top of the pack in three of the four early primary states, including Nevada.

And both are actively working to persuade voters that their approach is the better bet in a general election, including by appealing to voters who feel alienated from the political system. “If the best that Democrats can offer is business as usual after Donald Trump, then Democrats will lose,” Ms. Warren said at a campaign stop here on Sunday afternoon. “We win when we have solutions for the problems in people’s lives.”

Andrea Griffin, an elementary school nurse in Las Vegas, said she had been wary of Ms. Warren as a general-election candidate but came away feeling more confident after watching her on Sunday.

“I was a little skeptical about a plan for everything, but she has a pretty good grasp on what the major issues are and I kind of think that she might be able to get it done,” said Ms. Griffin, 56, a former independent voter who said she registered as a Democrat two weeks ago.

Ms. Griffin said she was also curious about Mr. Buttigieg, but had essentially ruled out Mr. Biden, explaining, “I think America is not ready to go back to business as usual.”