Climate policies have traditionally been a tough campaign issue for candidates. A mounting stack of scientific evidence has concluded that human activities — particularly burning coal and oil for electricity and transportation — are trapping heat in the atmosphere and leading to dangerous food and water shortages, increasing droughts and deluges, and potentially devastating sea-level rises. But Many American voters remain unconvinced that the science is real.

Since 2010, Republican campaigns have attacked Democrats who support climate policies to cut carbon pollution as backing a “war on coal” and “job-killing regulations.”

That kind of language is likely to escalate after June 2, when President Obama is expected to announce a climate change regulation intended to slash pollution from coal-fired power plants.

Charles and David Koch, billionaire industrialist brothers, have put millions of dollars into advocacy groups and super PACs like Americans for Prosperity, which have campaigned aggressively against lawmakers who support climate change policy.

“The left knows that the global warming agenda is a loser for them with the American people,” Tim Phillips, president of Americans for Prosperity, said in an interview. Mr. Phillips said that none of the four most vulnerable Democratic senators — Mary L. Landrieu of Louisiana, Mark Begich of Alaska, Kay Hagan of North Carolina and Mark Pryor of Arkansas — had embraced climate change policy. All four support construction of the Keystone XL oil pipeline, which Mr. Steyer opposes.

“Senators up for re-election have their sneakers on and are running from this,” Mr. Phillips said. “They know the issue doesn’t matter with most Americans.”

But one expert said Mr. Steyer’s tactic may work.

“Independent voters, with regard to the issue of climate change, track much more closely with Democrats than Republicans,” said Edward Maibach, the director of the Center for Climate Change Communication at George Mason University. “Painting candidates as climate deniers stands a good chance of working in districts where the vote turns on independents.”