A bipartisan, bicameral group of lawmakers on Wednesday called for a constitutional amendment requiring that Senators be replaced by a special election, rather than by gubernatorial appointment.

The effort, led by Sen. Russ Feingold (D-Wis.) and Rep. David Dreier (R-Calif.), comes as the Senate works through the sometimes difficult process of saying goodbye to sitting Senators and welcoming their gubernatorially appointed replacements.

At least five Senators have or are on the cusp of leaving the chamber to join President Barack Obama’s administration. In addition to Obama and Vice President Joseph Biden, Sens. Hillary Rodham Clinton (D-N.Y.), Ken Salazar (D-Colo.) and Judd Gregg (R-N.H.) have vacated or are about to vacate the Senate. In each case, a governor has or will appoint a new Senator.

Dreier said the proposed change to the Constitution is less a wholesale rewrite of the governing document, and more of a correction to the 17th Amendment, which puts the power of appointing Senators in the hands of a state’s chief executive.

“I’m convinced that the notion of appointments being left in the hands of the executive was merely an afterthought, and I believe that this effort we have here is merely completing the work of what was done with the 17th Amendment,” Dreier said.

Feingold noted that unlike in the Senate, House seats that become vacant midway through a Member’s term must be filled by a special election.

“The appointments in Illinois, Delaware and New York and soon New Hampshire have driven home that these decisions should be in the voters hand,” Feingold said.

“The appointment process itself is undemocratic.”

And while constitutional amendments usually face an uphill battle, early support from Judiciary Chairman John Conyers (D-Mich.) and the panel’s ranking member, Lamar Smith (R-Texas), could give the proposal some of the momentum it needs to stay off the cutting room floor.

Feingold said he hoped the Senate Judiciary Subcommittee on the Constitution would hold a hearing on the bill as early as March 10 or 11. Sens. John McCain (R-Ariz.) and Mark Begich (D-Alaska) have co-sponsored Feingold’s bill.

The 27th Amendment, which stipulates that Congress cannot change its compensation until after an election, was the last amendment ratified by the House and Senate, in 1992. It was first proposed in 1789, according to the National Archives.