As the presidential contest enters the final sprint, campaign aides and allies close to Vice President Kamala Harris are growing cautiously optimistic about her chances of victory, saying the race is shifting in her favor.

Top Democratic strategists are increasingly hopeful that the campaign’s attempts to cast former President Donald J. Trump as a fascist — paired with an expansive battleground-state operation and strength among female voters still energized by the end of federal abortion rights — will carry Ms. Harris to a narrow triumph. Even some close to Mr. Trump worry that the push to label him a budding dictator who has praised Hitler could move small but potentially meaningful numbers of persuadable voters.

Officials within the Harris campaign and people with whom they have shared candid assessments believe she remains in a solid position in the Northern “blue wall” states of Michigan, Pennsylvania and Wisconsin, saying internal polling shows her slightly ahead in all three — though by as little as half a percentage point.

They think she remains competitive across the four Sun Belt battleground states. Arizona and North Carolina appear to be the toughest swing states for Ms. Harris, these Democrats said, and they feel better about Georgia and Nevada.

Mr. Trump’s aides, for their part, believe that he can win at least one of the blue wall states, and that he remains competitive in all three. They are particularly hopeful about Pennsylvania, where members of his team say internal data shows him ahead, albeit within the margin of error. Some of Mr. Trump’s advisers are far more openly bullish, telling allies that he could sweep the seven battleground states.

This article is based on interviews with more than two dozen political strategists, campaign aides, pollsters and others close to the two campaigns and candidates, many of whom insisted on anonymity to discuss internal deliberations.