A coalition of nonprofit groups has started a campaign to exempt lobbyists for charitable and social welfare organizations that have tax-free status, meeting with presidential aides and sending them a package of ideas for rewriting the policy. Some senior officials privately agree with the effort, concluding that they are hurting the administration by effectively barring people who lobbied on behalf of human rights, environmental and consumer causes espoused by Mr. Obama.

Image Tom Malinowski, the Washington advocacy director for Human Rights Watch. Credit... Kim Jun-Ho/Yonhap

But White House officials said there had been no internal debate on the matter and flatly dismissed the proposals, adding that they would not consider any changes because it would start the administration down a slippery slope of declaring some lobbyists acceptable and others unacceptable.

“You can’t have a value judgment,” said Rahm Emanuel, the White House chief of staff.

David Axelrod, the president’s senior adviser, said Mr. Obama understood the tradeoff. Public trust in government is so fragile, he said, that it was important to stick to the campaign promise.

“It’s painful,” Mr. Axelrod said. “There are a lot of good people out there who are philosophically simpatico with us and are very skilled and would be very valuable to us.”

But, he said, “you can’t have carve-outs for lobbyists you like and exclude those that you don’t. It would be very hard for people to understand that distinction. This is one of those cases where we’ve had to sacrifice the help of a lot of very valuable people.”

Mr. Obama signed his lobbying order on his first full day in office, banning anyone who was a registered lobbyist from working for any executive agency they had lobbied in the past two years or in any other agency on an issue they had lobbied on in that time. As a practical matter, the order meant that most registered lobbyists could not take jobs in their areas of expertise. The policy was praised as “groundbreaking” in a letter from groups like Common Cause and the League of Women Voters.

The White House has granted three waivers, the first to William J. Lynn, a Raytheon lobbyist who became deputy defense secretary. The other two went to Cecilia Muñoz of the National Council of La Raza, who is now White House director of intergovernmental affairs, and Jocelyn Frye of the National Partnership for Women and Families, who is now Michelle Obama’s policy director.