Among the leaders the groups are pressing Mr. Biden to appoint, for instance, are Ms. Warren as Treasury secretary and Mr. Sanders as labor secretary — both standard-bearers of the progressive movement whose policies are viewed by some Democrats as too extreme.

Ms. Warren and Mr. Sanders are both said to be interested in the jobs. But appointing them to top government posts would be complicated by the fact that the states they represent, Massachusetts and Vermont, are led by Republican governors, and Democrats would want to make sure that any replacements would caucus with them to keep the balance of the Senate intact.

Also on the groups’ list are:

Representative Barbara Lee of California for secretary of state

Keith Ellison, the attorney general of Minnesota, for attorney general

Representative Rashida Tlaib of Michigan, one of the four congresswomen known as the Squad, for secretary of housing and urban development