Yes, as should be the speech of each person who points out the politician is lying.
A prerequisite for a politician to experience consequences for lying is for people to be free to discuss the lie, persuade fellow voters that he is lying, and disseminate that fact freely.
You’re not going to prevent politicians from lying by limiting speech. You’ll achieve quite the opposite effect, actually.
Free speech doesn't mean consequence free speech. Someone aspiring to public office should be penalised for deliberately misleading voters. The imbalance of power and exposure means that the many people who correctly point out the lies and manipulation are unheard, while the perpetrator of the lies and manipulation can freely continue to lie and manipulate.
They will be penalized, by the voters, if people are allowed to discuss the politician’s actions and statements freely and make their own judgement about his fitness for office, and if they actually choose to do so.
Ask yourself why those voices of truth go unheard. Or why the politician’s lies continue without consequence. Is it not because of a lack of robust speech around the politician’s behavior?
Why doesn’t that robust speech occur? Sometimes it is suppressed. But more often, the root of the problem is that most people prefer to be lied to. Seeking and discovering the truth is hard work, and it is work that no person should outsource to a third party. Yet that is exactly what people do, when they rely on the press or media for the truth. Those organizations lie at least as frequently as the politician does.
A prerequisite for a politician to experience consequences for lying is for people to be free to discuss the lie, persuade fellow voters that he is lying, and disseminate that fact freely.
You’re not going to prevent politicians from lying by limiting speech. You’ll achieve quite the opposite effect, actually.