“This is just wrong,” Mr. Wertheimer said of the auction to have coffee with Ms. Trump. “The president’s family should not be out raising money for whatever cause, in exchange for a potential influence buyer who wants to get his views to the president.”

Time with Ms. Trump clearly comes at a premium. Tony Podesta, a lobbyist and the brother of Hillary Clinton’s campaign chairman, John D. Podesta, also happens to be on the same Charitybuzz website offering lunch in exchange for a charitable donation.

The Podesta auction closed on Thursday with Tony Podesta, whose firm calls itself “A King of K Street,” having drawn just four bids, reaching $1,750 a couple of hours before it closed. The final bidding price is not public.

“Not a surprise that more people want to meet her than me,” Tony Podesta said in an interview Thursday. “She is sort of priceless right now. She is a great businesswoman. She is a really interesting person, and she is right in the middle of what is the biggest political change the United States has gone through since Roosevelt.”

Ms. Trump, who is disengaging from the Trump Organization where she is executive vice president, has signaled a desire to be involved in policy, working on pay equity for women and talking to her father about climate change.

She has interviewed candidates to work for her as chief of staff as she prepares for a possible role in the administration. She also plans to lobby members of Congress, in conjunction with the Republican Main Street Partnership, to expand child care, said Sarah Chamberlain, the partnership’s president. “We are thrilled to have her,” Ms. Chamberlain said Thursday.