But the shortfall is leaving Mr. Trump extraordinarily dependent on the Republican National Committee, which has seen record fund-raising this campaign cycle and, long before Mr. Trump even declared his upstart candidacy, had begun investing heavily in a long-range plan to bolster the party's technical and organizational capacity.
In a first for a major party nominee, Mr. Trump has suggested he will leave the crucial task of field organizing in swing states to the Republican National Committee, which typically relies on the party's nominee to help fund, direct and staff national Republican political efforts. His decision threatens to leave the party with significant shortfalls of money and manpower: On Monday, the party reported raising $13 million during May, about a third of the money it raised in May 2012, when Mitt Romney led the ticket.
"It's like a waterfall," said Brian O. Walsh, a Republican campaign strategist. "There are things that have to happen, and someone has to pay for them."
Mr. Trump's cash crunch marks a stark reversal from the 2012 presidential campaign, which seemed to inaugurate a new era of virtually unlimited money in American politics, buoyed by the Supreme Court's Citizens United decision two years earlier. By the same point that year, President Obama and Mr. Romney were raising tens of millions of dollars per month with their parties. And while Mr. Romney faced a larger deficit overall against Mr. Obama in June 2012, he was raising far more money than Mr. Trump is now, with big donors flocking to his cause.
"The campaign has got to be the entity that's out there driving the fund-raising car," said Austin Barbour, a lobbyist who served as national finance co-chairman of the Romney campaign. "And it better be a big old Cadillac."
Mr. Trump has defied conventional wisdom before, clinching the Republican nomination with a small organization and modest outlays on television. And Republican officials believe they are well prepared to compensate for Mr. Trump's late start. The Republican National Committee has more than 500 field staff members on the ground in swing states, far more than in 2012, and a robust digital and data operation.
Allies of Mr. Trump say they believe the tide is already turning. On Tuesday, Mr. Trump will appear at a high-dollar fund-raiser in New York City hosted by some of the most prominent names on Wall Street.
Fund-raisers for Mr. Trump, who asked for anonymity to discuss internal discussions, said they were now hoping to raise up to $500 million in joint efforts with the Republican National Committee, or an average of $100 million a month from June through October. He is now reliably raising between $5 million and $7 million in each city where he raises money, those donors said.
A joint fund-raising effort with Mr. Trump and 11 state Republican parties yielded the Republican National Committee $3 million in just five days at the end of May. Some of the largest checks came from a handful of wealthy Trump supporters who are not party mainstays, suggesting Mr. Trump could tap new sources of campaign money.
But Mr. Romney was also backed by expansive network of deep-pocketed "super PACs" and other outside groups that collectively spent hundreds of millions of dollars in an effort to elect him. This year, the Democrats are leading in outside money. Priorities USA Action, a group focused on advertising in support of Mrs. Clinton, announced on Monday that it had raised $12 million in May and had $52 million on hand — a huge reserve.
The outside spending effort to help Mr. Trump, by contrast, has been chaotic and underfunded, hampered by a profusion of competing groups, one of which has spent only $1 million so far on Mr. Trump's behalf.
The most prominent group, Great America, is advised by Ed Rollins, who managed Ronald Reagan's 1984 campaign, and other more seasoned Republican operatives. But it, too, has had difficulty persuading big donors: On Monday, it reported raising just $1.4 million during the month of May.
Fund-raising efforts for Mr. Trump have been hampered by the candidate's own erratic public comments. He has repeatedly said he will pay for his own campaign even as his volunteers fan out around the country to solicit six-figure checks, confusing allies and potential donors alike.
"Two days ago, he said, 'I may fund it myself,'" Mr. Rollins said. "Donors are all being cautious about what's going to happen here."