By Peter Nicholas of the Wall Street Journal

Sunday, February 10, 2013, 9:39 a.m. ET

Face-to-face with President Barack Obama at a Las Vegas event last month, Hector Sanchez seized the moment to make a plea: Would the president make room in his cabinet for more Hispanics?

"Don't worry, we're working on that," Mr. Obama said, according to Mr. Sanchez, chairman of the National Hispanic Leadership Agenda, a coalition of advocacy groups.

With the number of open cabinet seats dwindling, representatives of various parts of Mr. Obama's coalition are lobbying more intensively to make sure they are represented in the president's inner circle.

The leader of the Congressional Black Caucus, Rep. Marcia Fudge (D., Ohio), this week sent the president a letter asking him to nominate caucus member Rep. James Clyburn (D., S.C.) to be transportation secretary.

The Hispanic coalition wants Mr. Obama to appoint as many as three Latinos to his cabinet. Last month, the group sent a letter to the president suggesting a pool of 19 Latinos for him to consider.

Mr. Obama's cabinet includes the heads of 15 departments, Vice President Joe Biden and seven other officials. Of the 15 department-head posts, eight came open in recent months. The president has nominated successors for all but four: the secretaries of labor, energy, commerce and transportation.

Other important jobs he has yet to fill include chief of the Environmental Protection Agency, as administrator Lisa Jackson is expected to leave office later this month.

Racial and ethnic considerations are front-and-center in the jockeying for positions, an ironic predicament for a president who broke the ultimate racial barrier. As he fills out his second-term team, Mr. Obama is facing criticism that the people at the highest levels of his administration don't reflect the nation's racial and gender diversity or the coalition that helped him win two presidential elections.

Mr. Obama has picked white men for three of the most influential cabinet offices—the secretaries of state, Treasury and defense—and chosen another, Denis McDonough, to be his new chief of staff.

The White House appears close to nominating a woman as director of the Office of Management and Budget, a cabinet-rank post. The leading candidate is Sylvia Mathews Burwell, president of the Walmart Foundation and a Clinton administration veteran.

Jeffrey Zients, who is the OMB's deputy director and has been acting in the top post for more than a year, is the leading candidate to become the next U.S. trade representative.

Mike Froman, the White House's top international economics adviser, had been rumored to be in the running for the post of U.S. trade representative, which carries cabinet rank. But he is likely to stay in his current role, advising the president on a broad portfolio of issues, including trade, energy, climate and international-finance policy, a person familiar with the matter said.

Of the two Latino members of the president's first-term cabinet, Hilda Solis has left her post leading the Labor Department, and Interior Secretary Ken Salazar is departing soon. Mr. Obama has already named a white woman, Sally Jewell, to succeed Mr. Salazar.

"The window is closing, and we're getting concerned, because he keeps nominating people to the cabinet, and there are less and less options and possibilities,'' said Mr. Sanchez. "We still don't see any single Latino candidate being nominated, so that's why we're really putting extra pressure on the administration."

African-Americans, the heart of the president's electoral base, are also putting forward potential candidates as their numbers in the Obama cabinet shrink.

Attorney General Eric Holder is the highest-ranking African-American in the president's cabinet. He is expected to step down later this year, thinning the ranks of African-Americans in the cabinet.

Two other African-Americans of cabinet rank, U.S. Trade Representative Ron Kirk and Ms. Jackson, the EPA administrator, are also expected to leave office this month.

Jay Carney, the White House press secretary, said in an interview Friday: "There's not a numerical target here. This is about putting together a cabinet that will serve the president and the country well. And as part of that, the president values diversity, because he believes diversity improves excellence and enhances debate and decision-making."

Terry O'Neill, president of the National Organization for Women, said she was pleased the president had nominated Ms. Jewell to lead the Interior Department and that he was considering another woman, Penny Pritzker, for commerce secretary. She said she would like to see more women included in the president's inner circle.

She said that while there are "guys who can walk right in" to see Mr. Obama, "there needs to be girls who can walk right in, too."

Mr. Obama has only so many high-level jobs to fill—a reality that puts members of his coalition in competition with one another.

In filling the vacant post of labor secretary, for example, the White House is considering Edward Montgomery, an African-American who is dean of the Georgetown Public Policy Institute. Another person in the mix is a Latino, Joe Garcia, the lieutenant governor of Colorado.

—Damian Paletta contributed to this article.

A version of this article appeared February 9, 2013, on page A4 in the U.S. edition of The Wall Street Journal, with the headline: Groups in Coalition Ask Obama for Posts.