Also, the general issue with "liar" is "people wouldn't die for a lie!" which is manifestly untrue. People die for false causes all the time.
In fairness, the claim is a little more sophisticated than that: it's that people wouldn't die for a lie
that they knew to be a lie. Even the least perceptive apologists understand that while (e.g.) Islam is in their eyes a lie, many people believe in it and give their lives for it.
Where the argument has more traction is in the case of the apostles. If Jesus were not the Messiah, many of the other claims associated with him would have to have been invented by his closest followers. Similarly, if Jesus had never existed it's the apostles who would have invented him. In each case, the apostles and the other early Christians would have known that the story was partly or wholly false. And, the argument goes, many of those same early Christians were martyred.
Of course, it isn't true. The apostles in the gospels are no more real than Jesus, and the martyrdom stories for them and for the early leaders of the church are also false, at least during the time when the movement was getting started.