Hillary Rodham Clinton’s presidential campaign has been slow to harness the fund-raising power of the Democratic Party’s legions of grass-roots donors, according to reports filed Wednesday, a weakness that her campaign is racing to combat.

Of the $47.5 million that Mrs. Clinton has raised, less than one-fifth has come from donations of $200 or less. That is a far smaller proportion than that of her Democratic and Republican rivals who have excited grass-roots donors on the left and right, such as Senators Bernie Sanders of Vermont and Ted Cruz of Texas. While Mr. Sanders raised far less than Mrs. Clinton over all — about $15 million, including money transferred from his Senate account — about four-fifths of that amount came from smaller donors.

The slow response of grass-roots donors is a consequence, Mrs. Clinton’s aides and advisers said, of the deliberately low-key approach she has taken on the campaign trail — with few of the big rallies and campaign events that can help build voter lists and drive donations — along with the challenge in persuading some donors that Mrs. Clinton, who is far ahead in primary polls, needs their money.

The deficit could represent a financial and strategic liability for Mrs. Clinton if she were to win the nomination. The pool of Republican donors willing to write the maximum $2,700 check has grown so large that no Democrat, not even Mrs. Clinton, is likely to be able to match a mainstream Republican nominee on high-dollar fund-raising over the long term. In 2012, President Obama and his party were able to match the Republican candidate, Mitt Romney, only by raising far more money than Mr. Romney from small donors.