Money has been pouring in from all sides. Ms. Ocasio-Cortez, a New York Democrat, has raised $17.3 million, much of it from small donors attracted to her star power, progressive policies and outsize social media presence.

Her Republican challenger, John Cummings, a 60-year-old former schoolteacher at St. Raymond High School for Boys in the Bronx and a former officer for the New York Police Department, has collected $9.6 million in his first bid for office.

His campaign war chest exceeds all but a dozen or so House incumbents. He has a donor list any fund-raiser would envy. And over the last three-month reporting period, Mr. Cummings actually took in more money than Ms. Ocasio-Cortez, raising $5.5 million to her roughly $4 million…

Mr. Cummings has made heavy digital and cable advertising buys, blanketing his district, which covers parts of Queens and the Bronx, and even some areas outside it. He has hired consultants like Lincoln Strategy Group, an Arizona-based firm whose founder, Nathan Sproul, a longtime Republican operative, has faced fraud accusations over the years.