At an appearance in New Hampshire over the weekend, he told a crowd of about 60, “This is a tremendous turnout,” a bit of campaign flattery, but one that drew attention to the fact that hundreds line up for better-known candidates.

Mr. Inslee, whose father was a science teacher, has been an advocate for action on climate change for decades. He has a ready explanation for why he is not polling higher: It is early in the primary marathon, and as a Western governor he lacks a national profile.

“The history of these things is successful, accomplished governors start at 1 percent,” he said in an interview. “That’s where Bill Clinton and Jimmy Carter started their climbs.”

Mr. Inslee insists he will gain prominence as more voters learn of his record and his meaty policy proposals, which are getting high marks from activists. On Friday, at a youth climate protest in Las Vegas, he shared evidence of momentum: he had just logged his 65,000th donor, ensuring Mr. Inslee a place in the first Democratic debate next month. His campaign said donors increased by more than 35 percent after he released his first climate plan on May 3.

Representative Alexandria Ocasio-Cortez, a co-author of the Green New Deal resolution in Congress, told her four million Twitter followers last week that Mr. Inslee’s climate plan was “the most serious + comprehensive” by any candidate.