Former Rep. Pete Hoekstra, who is running for Senate in Michigan, has come under fire from Democrats for suggesting repealing the 17th Amendment.
The framers designed the Constitution to have state legislators select Senators in order to strengthen the power of state governments. The theory was that Senators dependent on the state government for reappointment would not support taking too much power away from the states.
"It is recommended by the double advantage of favoring a select appointment, and of giving to the State governments such an agency in the formation of the federal government as must secure the authority of the former, and may form a convenient link between the two systems," James Madison wrote when he addressed the question in the Federalist Papers.
Mourdock said another benefit of appointing Senators would be to reduce the influence of campaign money.
"In today's world, we see millions and millions of dollars spent on Senate campaigns," Mourdock said. "Two years ago, in 2010, Sharron Angle out in Nevada spent $31 million dollars, just herself. How much money would be spent in federal Senate races if the state legislators were electing those people. You just took the money out of politics."
However, the progressive movement of the early 20th century pushed to require that Senators be popularly elected precisely because money had become a corrupting force within the state legislatures.
State legislatures and potential Senators regularly faced charges of buying and selling Senate seats. The Senate historical office has written that bribery became a common occurrence and part of the game.
For instance, with the states soon to consider the constitutional amendment to subject Senators to the voters, the Senate expelled Sen. William Lorimer (R-Ill.) in 1912. Newspapers discovered that supporters paid about $100,000 to secure the selection of Lorimer by the Illinois Legislature.
In many states, Senate seats that become vacant during a term may still be filled by appointment, as was the case when former Illinois Gov. Rod Blagojevich appointed fellow Democrat Roland Burris to serve out the term of President Barack Obama apparently after being unable to find a bidder for the office.
Based on the pay schedule from the Lorimer case, Balgojevich may have undervalued the Senate seat. Federal investigators found Blagojevich was seeking $1.5 million in benefits and contributions for the seat. By contrast, Lorimer's associates would have paid almost $2.4 million in today's money for the office.
Blagojevich was sentenced in December to 14 years in federal prison after being convicted of public corruption charges, including the scheme to sell the Senate seat.
The questions about the way Senators are elected did not originate this cycle.
Sen. Mike Lee (R-Utah) told CNN as a Senate candidate in July 2010 that he would support rolling back the constitutional change.
"I do think the 17th Amendment was a mistake," Lee said. "I do think that we lost something when we adopted it, but I don't think that in our lifetimes we're going to see any movement afoot to do that."