Senators are elected by the people in the state that they represent...Hence, a “representative republic”...
The Founders never meant for us to have a Representative Republic! They set up a Constitutional Republic!
The People were to be represented by the House of Representatives who were directly elected by the citizens of the country.
The States were to be represented by the Senators who were appointed by the legislatures of each state.
The House and Senate were expected to handle every aspect of governance for the nation, a Chief Executive was avoided since such a person could easily become a King in all but name.
See here https://freerepublic.com/focus/f-news/4071384/posts?page=80#80