But while Mr. Steyer did not poll high enough to make the debate stage this round after landing distant finishes in Iowa and New Hampshire, he has emerged as a genuine threat to a number of his rivals in South Carolina and, potentially, here in Nevada, as the largely self-funded candidate spends millions on the airwaves in both states.

He is also spending his money on splashy campaign events: On Friday, he is set to rally here with the group TLC, known for 1990s hits like “No Scrubs.”
Mr. Steyer, a spokesman said, was spending the evening meeting with precinct captains and making calls to his teams around the state to encourage them in the homestretch before the caucuses.

“Tonight’s debate helped one person — Donald Trump,” Mr. Steyer said in a statement after the debate, also saying it was “clear that Bloomberg is probably running in the wrong primary.”

“Instead of focusing on how we can improve the lives of Americans and build a diverse coalition to beat Donald Trump,” Mr. Steyer said, “we saw a lot of bickering over policy discrepancies that won’t matter if we don’t win in November.”