Senator Bernie Sanders would begin a 2020 presidential bid with 2.1 million online donors, a massive lead among low-dollar contributors that is roughly equivalent to the donor base of all the other Democratic hopefuls combined.

Beto O’Rourke, the former Texas congressman who narrowly lost a Senate race last year, is also poised to be a fund-raising phenom if he runs for president: He has twice as many online donors as anyone eyeing the race besides Mr. Sanders.

Three senators who are already running have their own solid track records with small donors. Senator Elizabeth Warren, with the third-highest number, has notable strength in New Hampshire, even topping Mr. O’Rourke there. Senator Kirsten Gillibrand has built up broad national support among small donors, despite a reputation as a big-money fund-raiser, while Senator Kamala Harris raised $1.5 million online in her first 24 hours as a presidential candidate.