And what would 'the public' do about it? There is no mechanism for recalling a President beyond impeachment. A President could walk out onto the White House lawn, pull a gun and off a Girl Scout, and there is nothing 'the public' could legally do. Unless Congress is willing to impeach that's all she wrote.
AFAIK, a President is not immune to criminal charges. If a sitting US President were to commit a crime, such as fraud or murder, there would be nothing to prevent him from being charged.