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But unlike Mr. Inslee, who governs in a liberal state, Mr. Bullock has made his political calling card that of a Democrat who has flourished in the rural West: He has been elected statewide three times, once for attorney general and twice in his bids for governor, each time in a year that his party’s presidential nominee was losing Montana.

“As a Democrat in a red state, I often spend days among crowds where there are almost no Democratic voters in sight,” he wrote in an opinion piece for The New York Times in 2017, adding that his party “should try casting the fly line a little farther out into the river.”

In his video, which featured clips of him across Montana, Mr. Bullock did not make the case for his electability directly, but said, “As a Democratic governor of a state that Trump won by 20 points, I don’t have the luxury of just talking to people who agree with me.”

Yet Mr. Bullock, who waited until his state’s legislative session ended to declare his presidential intentions, faces considerable challenges as he enters an already crowded Democratic field. He has little in the way of a fund-raising base, whether among wealthy donors or the party’s grass-roots base, and he could find it hard to break through the din at a time when celebrity and social media appeal have become central to presidential politics.

Mr. Bullock has repeatedly visited Iowa, and appears poised to have the support of the state’s long-serving Democratic attorney general, but has been there less often than some of his rivals, who have been in the race for months.

In addition to the structural impediments looming in his path, Mr. Bullock will also confront a challenge of his own making: the revelation that one of his former senior aides had been accused of sexually harassing several women. The aide, Kevin O’Brien, who worked for Mr. Bullock in Montana and in Washington when the governor ran the Democratic Governors Association, was fired from his role with the organization after an inquiry there revealed he had sexually harassed a female colleague.

Mr. Bullock knew why Mr. O’Brien was terminated but did not intercede to stop Mayor Bill de Blasio of New York from hiring him just weeks after his dismissal from the governors’ organization. And Mr. O’Brien would eventually be forced to resign from the mayor’s office after two more women accused him of sexual harassment.