MANCHESTER, N.H. — As Democrats consider Hillary Clinton’s candidacy for the second time, women are wrestling with a difficult question: whether they have an obligation to get behind someone who is closer than anyone has ever been to becoming the first female president.

And with her opponent, Senator Bernie Sanders of Vermont, outdrawing her in support among young women, Mrs. Clinton’s candidacy has turned into a generational clash, one that erupted this weekend when two feminist icons, Madeleine Albright and Gloria Steinem, called on young women who supported Mr. Sanders to essentially grow up and get with the program.

While introducing Mrs. Clinton at a rally in New Hampshire on Saturday, Ms. Albright, 78, the first female secretary of state, talked about the importance of electing a woman to the country’s highest office. In a dig at the “revolution” that Mr. Sanders, 74, often speaks of, she said the first female commander in chief would be a true revolution. And she scolded any woman who felt otherwise.

“We can tell our story of how we climbed the ladder, and a lot of you younger women think it’s done,” Ms. Albright said of the broader fight for women’s equality. “It’s not done. There’s a special place in hell for women who don’t help each other!”