Mr. Greene has been tapped by the White House to serve as assistant secretary for policy development and research, pending Senate confirmation. Similarly, if confirmed, Mr. Colón is slated to lead HUD’s community planning and development portfolio. To date, both men have drawn the scrutiny of GOP lawmakers on the Senate Banking, Housing and Urban Affairs Committee, of which Mr. Toomey is the ranking member, for their longstanding and inflammatory statements on social media. Mr. Colón, who serves as a housing official in New York, previously used his Twitter account to routinely disparage members of Congress, “cabinet officials, Republican voters, and news anchors,” according to the letter.