Ms. Ocasio-Cortez’s campaign, in particular, has become a cause célèbre for some on the left who seem set to put a scare into Mr. Crowley, the head of the Queens Democratic Party, one of the last and most powerful political machines remaining in New York. MoveOn.org and Our Revolution, an outgrowth of the Sanders campaign, both endorsed her, and the news site The Intercept has generated a drumbeat of negative stories on Mr. Crowley.

Earlier this week, she showed up to debate Mr. Crowley, the potential future leader of House Democrats in Washington — only to discover that he was a no-show, a Latina surrogate sent in his place. (Mr. Crowley had debated her earlier this month.)

“We have a political culture of intimidation, of favoring, of patronage and of fear and that is no way for a community to be governed,” Ms. Ocasio-Cortez said.

Lauren French, a spokeswoman for Mr. Crowley, predicted victory next week because the congressman “is unapologetically fighting for the people of Queens and the Bronx — communities that need health care, affordable housing, gun safety laws, immigration reform and better jobs with higher wages.”

Mr. Patel has waged the most millennial of campaigns. On a recent Thursday evening, he was sitting in a former bar in the East Village that he uses as his campaign headquarters. His campaign manager handed him one of three phones that was logged into the dating app Tinder, and Mr. Patel began furiously swiping right.

All around the bar — adorned with blue-velvet booths and a sound system that was playing Kanye West — campaign volunteers, logged onto Tinder, Grindr or Bumble, were doing the same thing. Mr. Patel calls it Tinder banking: Participants set up an account with a picture of an attractive person, usually not themselves, and begin seeking matches. Mr. Patel uses a picture of his brother.