Amendment 17 - Senators Elected by Popular Vote. Ratified 4/8/1913. History
The Senate of the United States shall be composed of two Senators from each State, elected by the people thereof, for six years; and each Senator shall have one vote. The electors in each State shall have the qualifications requisite for electors of the most numerous branch of the State legislatures.
When vacancies happen in the representation of any State in the Senate, the executive authority of such State shall issue writs of election to fill such vacancies: Provided, That the legislature of any State may empower the executive thereof to make temporary appointments until the people fill the vacancies by election as the legislature may direct.
This amendment shall not be so construed as to affect the election or term of any Senator chosen before it becomes valid as part of the Constitution.
http://www.usconstitution.net/const.html#Am17Remember the Blagojevich case? That was about Blagojevich's authority to appoint a new senator to replace Obama.
However, only five states (Wisconsin, Massachusetts, Oregon, Alaska and Oklahomna) require special elections to fill vacant Senate seats. The other 45 states allow their governors to appoint Senators when seats become vacant. The contentious appointment of Sen. Roland Burris (D-IL) by former Gov. Rod Blagojevich of Illinois to fill the vacancy left by President Obama has brought the constitutional issue to the forefront.
http://www.examiner.com/x-6489-Madison-Political-Buzz-Examiner~y2009m8d10-Should-governors-be-allowed-to-appoint-US-senators-to-fill-vacanciesApparently Senator Feingold introduced a bill to require special elections in all states. There would be an election in Massachusetts. Here we go again.