Political Controls on Agency Action
This is the most important restriction on public health authority. From the surgeon general of the United States to the health officer in the smallest town, every public health official works for politicians. In some cases they work for independent boards, rather than directly for the elected officials, but the end results are the same.
Agencies are the mechanism by which political decisions are carried out.  The fundamental control over agency actions is through the election of the official that oversees the agency.  Political control is exercised by the head of the executive branch giving orders to the agency director or replacing the agency director.   Legislatures may insulate agencies from direct political action by having them answer to a board or commission that is appointed by the executive. The members of this board have fixed terms and can only be replaced when their term expires.  This limits the political pressure the executive can put on the agency.  At the federal level, the Securities and Exchange Commission is an independent agency.  Some state and local health officers work for a board of health that provides greater or lesser protection from political influence.
Agencies may be part of the executive branch, but they are funded and authorized by the legislature.  The legislature can direct agencies to carry out actions through statute or funding, and legislatures can block agency actions by statutory or funding changes.  Even independent agencies such as health departments under boards of health are under the control of the legislature.  As long as an agency is operating within its enabling law and the constitution, courts defer to the agency because it is carrying out legislative goals. The courts often remind persons who are challenging agency actions that the proper way to change agency behavior is through the legislature.
Public health officers who take actions that are politically unpopular in their community will be forced out of office. Public health officers also cannot do anything that elected officials will not pay for. For example, attempts to quarantine everyone with AIDS or other communicable diseases would be impossibly expensive as well as politically suicidal. Even with the resurgence of tuberculosis, it is politically difficult to get support and resources for confinement when it is necessary to treat an individual and prevent spread of the infection.
Public health agencies face two critical political threats.  First, is the pressure to change public health policy to satisfy political agendas that are not based on good public health principles.  At one time, health departments faced pressure to use public health powers to carry out racially discriminatory policies.  A current example is the refusal of many states to do proper contact tracing and reporting of HIV because of the lobbying by privacy advocates.
The second threat is more insidious and pervasive - the pressure by the executive and the legislature to keep public health problems out of the news and to reassure the public that everything is fine.  This reduces pressure to raise taxes or divert money from other areas to pay for public health services.  Even when health directors know that they are unable to deal with critical problems, such as responding to emergencies, they know that raising these issues will often cost them their jobs.[Institute of Medicine, 1988. The Future of Public Health. National Academy Press: Washington, DC]