"second the motion" comes from language that is used in meetings or groups. In certain meetings, there are rules around how to make a decision.
In some formal meetings, if someone wants the group to make a decision, that person will say "I move that we ________ (buy a car, jump up and down, go to Florida - whatever the group needs to decide to do.)" which means that the person thinks the group should decide to do the thing. If another person in the meeting agrees with that suggestion, they will say "I second the motion." which means "I agree that we should _______." If no one seconds the motion, it means that everyone thinks the idea is stupid and the group shouldn't do it.
So the person feels exhausted. He's doesn't think he can do this and wants to make the decision to stop trying. He's looking for someone to agree with his opinion and he's using the language around meetings to express that thought.