Ethan Todras-Whitehill, executive director of the nascent political action group Swing Left, stood near the staircase inside the lobby of the St. James Theater in Manhattan, home of the musical “Frozen.” It was a Tuesday afternoon in mid-June, and the bearded Mr. Todras-Whitehill was dressed in jeans and a blue blazer, as well as a new shirt bought earlier that day at H & M after the one he’d been wearing was deemed unacceptable for television. (There was a crew from MSNBC in attendance.)

Mr. Todras-Whitehill seemed unbothered by the subtle change in attire. Since he and two close friends — none of whom then worked in politics — led the formal launch of Swing Left in January 2017 with the aim of flipping the House of Representatives to Democratic control in the 2018 midterms, Mr. Todras-Whitehill has quickly acclimated to his newfound prominence in the world of grass-roots politics.

Swing Left’s mission of identifying 78 swing districts, 23 of which would have to be flipped in order to return the Democrats to power in the House, has found a receptive audience. The group has more than 400,000 members and has raised more than $9 million in donations so far.

Over the past year, Swing Left has drawn unsettled Democrats across the country, including a number of so-called influencers, to its ranks, even as more well-funded groups have entered the fray, including the one recently started by Michael R. Bloomberg and Tech for Campaigns, a volunteer network consisting of more than 4,500 tech workers at companies like Google, Facebook and Netflix. And it’s reinforced the notion, illustrated most starkly by the 2016 presidential election, that the traditional ways of running a campaign are increasingly irrelevant.