The Court of Appeals for the District of Columbia held yesterday in PHH Corporation v. Consumer Financial Protection Bureau that independent agencies with a single head appointed for a fixed term of office are constitutional. The argument was that this arrangement encroaches on the President's constitutional powers. If you thought that the question of whether independent agencies are constitutional had been decided in the affirmative during the New Deal, you'd be right when it comes to independent agencies headed by a multi-member board but there has never been any decision on the issue when it comes to independent agencies headed with a single head appointed to a fixed term of office. I really don't see the distinction and neither did this Court but I expect that the right wing effort to wipe out independent agencies will continue. This particular issue may eventually come before the Supreme Court.
Of course, the Social Security Administration is an independent agency with a single head appointed for a fixed term of office. However, it would be hard to raise the constitutionality issue now for the Social Security Administration because the agency currently has an acting Commissioner who could be removed by the President at any time.