Mrs. Clinton has had problems attracting millennials throughout her campaign. Senator Bernie Sanders of Vermont outperformed her among young voters in the Democratic primary, and many of them are shunning the two major political parties in the general election.

However, John Della Volpe, the director of polling at the Institute of Politics, said Mrs. Clinton had made some gains since the summer because many millennials watched the presidential debates and liked how she handled Mr. Trump. He also said that Mr. Johnson’s gaffes about Syria and world leaders had hurt his standing and that Mrs. Clinton had benefited from his troubles.

“The combination of her performing better than expectations during the debates with Donald Trump, and Gary Johnson disappointing voters, has left her in a position where she has increased the number of people who view her favorably,” Mr. Della Volpe said. “But she still has progress to make if she’s going to unite the most progressive wing of the party, moderates and even Republicans.”

Signs of that challenge can be seen in the number of young voters concerned that she may not be able to improve crucial parts of society. Just 47 percent of the young Americans Harvard surveyed said they trusted her more than Mr. Trump to improve the economy, and 46 percent said they trusted her more to combat the spread of terrorism. Only 42 percent trust her more than her opponent to reduce the impact of money in politics, as she continues to push back against the perception that she is too closely tied to Wall Street.