(Bloomberg) -- President-elect Joe Biden’s early picks for top administration jobs made history for elevating women, people of color and immigrants. But advocates want to see more racial diversity closer to the center of power, putting pressure on Biden as he moves to a new round of selections next week.He is now drawing criticism over the makeup of his inner circle from Black and Latino lawmakers, and groups like the NAACP and UnidosUS are demanding more say on selections. Amid those objections, his transition team slowed its decision on a Defense secretary, and its choice of a health secretary is emerging as a new flashpoint before an announcement as soon as next week.The incoming administration broke major barriers with the selection of Kamala Harris as the first Black and Indian-American woman for vice president, along with two Black women, a Latino immigrant and an Indian-American woman for key economic and national security posts. Yet advocates say those officials won’t be as close to the seat of power as the White people the president-elect chose for key posts -- including Janet Yellen for Treasury Secretary, Antony Blinken for Secretary of State and Ron Klain as chief of staff.“The reality is that there are not enough Black people in his inner circle,” said David Clunie, the executive director of the Black Economic Alliance and a former Obama administration official.He urged Biden to make sure Harris and Louisiana Congressman Cedric Richmond, who’s joining the administration as a senior adviser and director of the Office of Public Engagement, are included in his key decisions. Harris said in a CNN interview Thursday that Biden “wants me to be the first and the last in the room.”Biden acknowledged, and even welcomed, the pressure and promised to follow through.“I promise you, it will be the single most diverse cabinet based on race, color, based on gender that’s ever existed in the United States of America,” he said at a Friday press conference. Pressed on whether he’d be choosing people of color as Defense secretary and attorney general, he declined to say.He said in a CNN interview on Thursday that he was hearing from advocacy groups but recognized “it’s their job to push me.”Latino advocates have been pressing top Biden advisers to choose New Mexico Governor Michelle Lujan Grisham as Health and Human Services secretary after the transition team moved away from her for that position. In response, the Biden camp leaked to reporters that they had picked her for Interior secretary and that she turned them down in the hopes of getting HHS.When the Congressional Hispanic Caucus met with three of Biden’s top advisers on Thursday, members had believed Lujan Grisham was the most likely Latina to get a spot in the Biden cabinet and they publicly expressed dismay at the leaks suggesting she may not get a job at all.“This was to kind of throw her under the bus,” Arizona Representative Raul Grijalva said. During the meeting, “almost all the members commented on that, how they felt that that was a raw deal that the governor got -- that that kind of publicity was meant to undermine any effort of her getting HHS.”Klain and transition co-chairs Ted Kaufman and Jeff Zients told the CHC on Thursday they want Lujan Grisham in the administration, though they didn’t reveal whether she still had a shot at HHS, a Democrat on the call said.The growing concerns over the health-secretary position reflect the chagrin expressed by Representative James Clyburn of South Carolina and other Black lawmakers over the number of African Americans selected so far for key roles. This week, Biden unveiled his economic team during a press event in Wilmington, Delaware, including four women, one Black man and one White man -- with the cabinet-level jobs all going to women, including Yellen. All spoke of their humble beginnings and pledged to fight to close the wealth gap.Two days later, Biden announced in a written statement the appointment of a White man, Brian Deese, to head the National Economic Council. TIAA Chief Executive Officer Roger Ferguson, who is Black, had also been under consideration for the job. Deese is an executive at BlackRock Inc.Clyburn and other members of the Congressional Black Caucus have made clear their preference for Ohio Representative Marcia Fudge, who is Black, to be Agriculture secretary. The Congressional Asian Pacific American Caucus last month wrote to Biden asking him to include Asian Americans and Pacific Islanders in his cabinet.The Biden team slowed its selection process for Defense secretary after Black leaders expressed concerns that Biden might not name an African American to any of the top four cabinet departments -- Defense, Justice, State or Treasury. He had been widely expected to tap Michele Flournoy, who is White, to be the first female Pentagon chief, but she wasn’t announced with the rest of his national security team two weeks ago.Two Black candidates, retired four-star General Lloyd Austin and former Homeland Security Secretary Jeh Johnson, have been reported to be among those Biden is now considering to lead the Pentagon, and Johnson has also been discussed as an option for attorney general.Biden also faces pressure for diversity in political ideology. Progressive Democrats have also made clear their opposition to a range of potential picks and nominations, targeting people they see as potentially leading Biden away from his campaign promises to the left.“I don’t envy them,” Janet Murguia, president of UnidosUS, said of the Biden transition team. “This is a very challenging time in terms of meeting the commitments that have to be met.”‘Making Everybody Happy’Murguia, who worked in Bill Clinton’s White House, nevertheless said her expectations were high. “For some of us, we were part of administrations that had at least three or four Hispanics 25 years ago, 30 years ago. So the bar is very high in terms of making everybody happy,” she said. “I know that’s likely not going to be possible. I do understand that. But it also underscores why we have to keep promoting that high-water mark for representation.”Murguia asked Biden Thursday to meet to “discuss our shared goal of ensuring that government at all levels reflects the diversity of America and works well for all families.”She’s not alone in requesting a session with the president-elect. So have a coalition of Black civil rights groups including the NAACP and the National Urban League, who say they’re concerned about Black representation in key positions and want Biden to make clear that civil rights will be a central issue for his administration.“We want to make sure that issues concerned with civil rights is a top priority. And it’s not secondary and it’s not talking points,” said NAACP President Derrick Johnson, who is scheduled to meet with Biden on Tuesday.But Johnson added that he shouldn’t have had to ask for the meeting.“We shouldn’t have to guess what he’s thinking; it should be a direct line of communication,” he said, pointing out that Biden’s agency review teams include people from business, environmental and labor groups but not civil rights groups.A transition official said Biden’s team has been working with the NAACP Legal Defense Fund, which is independent of the NAACP, and the National Urban League. It’s also in regular contact with the Congressional Black Caucus, which is recommending personnel.Keeping Certain People OutThe advocates also are fighting to keep certain people out of the administration.At the top of their lists is Rahm Emanuel, the former Obama chief of staff and former Chicago mayor who is rumored to be under consideration for Transportation secretary or another post. They say he should be disqualified because of his handling of the response to the 2014 killing in Chicago of Laquan McDonald, an unarmed Black teenager, by a White police officer.“Is that the type of person you would want to have as a part of your legacy?” Johnson said.The transition declined to comment on whether Emanuel is under consideration for an administration job.(Adds earlier Harris comment in fifth paragraph.)For more articles like this, please visit us at bloomberg.comSubscribe now to stay ahead with the most trusted business news source.©2020 Bloomberg L.P.