Harming someone's reputation in speech with falsehoods is known as slander, and doing the same thing in writing is known as libel (which sometimes includes speech as well). Any ordinary citizen who can claim to have suffered harm as a result of such defamation may sue. So why aren't politicians suing all the time? Because an exception is made for "public persons" (a category that includes most other celebrities as well), who must also prove that any such statement was made with "reckless disregard for the truth". And although, even by that standard, public persons are defamed all the time, most of them have decided that it's better to just grin and bear it.