A carbon tax, however, faces major political challenges. Even in Mr. Inslee’s overwhelmingly blue state, measures he supported to price carbon failed three times in recent years.

“At the end of the day, you can get 300 economists to vote for it,” said John D. Podesta, a former top adviser to President Barack Obama and chairman of Hillary Clinton’s 2016 presidential campaign. “The question is, can you get 300 elected officials of any party to vote for it?”

With that difficulty in mind, several candidates pledged to return the revenue to the public in some form. Mr. Delaney, a former representative from Maryland who co-sponsored a carbon tax bill in the House, has the most specific plan: a tax starting at $15 per metric ton of carbon dioxide, increasing by $10 each year. All of the revenue would be returned to taxpayers, he said, “with an option to invest the dividend into a tax-advantaged savings account.”