But Mr. Kushner’s aggressive involvement has also been described as something of a defensive move: By positioning himself as the point person on raising money for the campaign, he prevents antagonists and potential rivals from taking over a job that comes with great power and proximity to the president.

Mr. Trump, for his part, has seemed uninterested in discussing the state of the fund-raising for 2020, or in hearing Mr. Kushner’s concerns at last month’s dinner. After regaling the group with stories about his foreign trips and past business ventures, the president left the meeting, declaring, “As long as we’re breaking records, I don’t care.”

A person close to Mr. Kushner, who was not authorized to speak publicly, insisted it was the president who had initially pitched the idea of a “thank you” dinner for staff members. But it morphed into an opportunity for Mr. Kushner, who has helped oversee an effort to attract more online small donors, to present himself to Mr. Trump as the person with the best solutions.

During the meal, Ms. McDaniel explained the party committee’s fund-raising goals for 2019, and Mr. Kushner countered that they were insufficient. For the last few months, people involved in fund-raising for the campaign have complained that it is hard to plan effectively when the White House gives little lead time for committing to dates. A major donor dinner in New York this month, for instance, was put together with just six days’ notice.

In a statement, Mr. Kushner said that he harbored no concerns about the committee’s performance. “The R.N.C. under Ronna’s leadership has done historic work and President Trump is well served with her at the helm,” he said.

And the committee, according to Michael Ahrens, a spokesman, “has a great working relationship with the team at the White House.” He added that it is “because of President Trump’s long list of accomplishments and the leadership of Chairwoman McDaniel that we’re able to break fund-raising records month after month.”