I know that Corker doesn’t know much about the Constitution, so someone should tell him that the Senate already has the power to ratify treaties. This vote that he is pushing for somehow diminishes the power that already exists.
There are treaties and then there are Executive Agreements. Obama is trying to basically do a treaty but call it an Executive Agreement so he avoids advise and consent by the Senate.
So now the Senate is trying to wrest back control by passing a piece of legislation for this particular instance. Its just cat and mouse but they have to do something or the guy is going to put the plane into the side of the mountain.