President Barack Obama’s second-term Cabinet continues to take shape, with Labor Secretary Hilda L. Solis resigning and three others deciding to stick around — Attorney General Eric H. Holder Jr., Health and Human Services Secretary Kathleen Sebelius and Veterans Affairs Secretary Eric Shinseki.

Solis’ exit came the same day as White House Press Secretary Jay Carney took pains to defend the administration’s record on promoting women to top jobs and comes after other high-profile women have decided to move on, including the EPA’s Lisa P. Jackson and Secretary of State Hillary Rodham Clinton. Senate Foreign Relations Chairman John Kerry has been nominated to replace Clinton.

The openings at the Labor department and the EPA are likely to prove contentious on Capitol Hill, as union rights and environmental regulations are among the fiercest fights around.

The trio sticking around was confirmed by a senior administration official, but the status of other Cabinet members is still uncertain. The process has started to accelerate after the president’s Hawaii vacation, with the fiscal cliff resolved for now and the president’s inauguration looming in less than two weeks.

The president is widely expected to name his Chief of Staff Jacob J. Lew to be Treasury Secretary on Thursday. Lew would join Kerry at State, former Sen. Chuck Hagel for Defense and John Brennan for CIA director as high-profile second-term nominations so far.