But for the growing number of nonprofit journalism organizations, the moment may provide the kind of opening they have needed to take on a much larger role for a field that continues to face significant financial challenges and sinking public trust.

Nonprofit newsrooms have long sought to position themselves as civic resources, relying on the same skills as newspapers and television stations, but without profit motives or a dependence on advertisers. As traditional news organizations with dwindling resources have curtailed their ambitions in recent years, nonprofit news groups have sought to pick up the expensive work of investigative and accountability journalism — though often with a fraction of the audience.

With a president-elect who has shown a willingness to attack the press, and a proliferation of fake news that has shaken the public’s confidence in the news media, news executives said the watchdog role would be more important than ever.

They also caution that the rush of small gifts is not necessarily a panacea for their own financial concerns. It remains to be seen if the higher level of individual giving will continue, or if it will extend to big donations through grants and wealthy individuals, who provide the bulk of the funding for groups like ProPublica and others.

Still, the signs are encouraging, especially when coupled with widely reported increases in engagement from readers and listeners, Mr. Tofel and several of his colleagues said.

At one point, after the comedian John Oliver promoted the organization on his HBO show, ProPublica was receiving as many as four donations a minute.