His allies say his deal-making skills lie in an ability to force battling factions to the table and then make them feel collectively responsible for a solution. He can also be an incrementalist, they say, demanding that adversaries move — but not too far or too fast.

As a candidate, Mr. Hickenlooper is pushing middle-of-the-road policies: Universal health care, but not a single-payer system. Swift action on climate change, but not the Green New Deal. He says he is likely to put a Republican in his cabinet and would choose a woman as his running mate.

He is also banking on his ability to charm.

He often speaks about growing up as a skinny, dyslexic kid who learned to neutralize bullies with humor; as an adult, he’s turned into his state’s gregarious geek-in-chief. His stump speeches are packed with self-effacing jokes, and friends say his deepest desire is to be liked — to connect with his audience.

This freewheeling personality has won him many a political and business deal. It has also caused him to fumble in ways that might be problematic if he were to get to the White House. He once introduced his lieutenant governor as a “rising sex star,” flubbing a joke in an audience of grade-schoolers, only to make a similar mistake a few days later. (It’s unclear what Mr. Hickenlooper was trying to say, though in the past he had called his deputy both a “rising star” and a “sex symbol.”)

Reporters have called these “Hickenbloopers.” Aides have called it his foot-in-mouth problem.

His skeptics have accused him of hiding behind compromise and using it to avoid taking firm stances on pressing issues. That criticism is sometimes lobbed at him when it comes to the environment.

As governor, Mr. Hickenlooper developed some of the country’s strictest oil and gas regulations, passed a first-in-the-nation methane capture rule and helped to make Colorado one of just 10 states to receive more than 20 percent of its electricity from renewables. On the campaign trail, he speaks often about the economic and moral incentive to move fast on climate change.