Article I, Section 6, of the Constitution says this: "No Senator or Representative shall, during the Time for which he was elected, be appointed to any civil Office under the Authority of the United States which shall have been created, or the Emoluments whereof shall have been increased during such time."
The word "Emoluments" is a reference to salary or compensation.
Senate Democrats are now working on legislation to pave the way for Clinton to become secretary of state, despite the clause. There is precedent for doing so: As the New York Times notes, "In the past, Congress has gotten around this by passing a resolution cutting the salary for the office at stake back to what it was before the nominee's most recent election."
The maneuver even has a name: The "Saxbe fix," named after Richard Nixon attorney general nominee Sen. William Saxbe. Bill Clinton also used the Saxbe fix when nominating Sen. Lloyd Bentsen as treasury secretary.
But Judicial Watch says the Saxbe Fix doesn't do the job, since "it cannot change the fact that the salary had been increased while Senator Clinton served in Congress."
"Simply put, the Constitution does not provide for a legislative remedy for the Ineligibility Clause," the group claims.
Clinton spokesman Philippe Reines dismissed the group's criticism.
"This is a Harvard Law grad nominating a Yale Law grad here, so all parties involved have been cognizant of this issue from the outset," he told the Times. "But putting frivolous lawsuits by fringe groups aside, this issue has been resolved many times over the past century involving both Democratic and Republican appointments and we're confident it will be here too."
And CBS News legal analyst Andrew Cohen doesn't expect it to be a serious issue.
"This is a non-story raised by the same people who hounded the Clintons a decade ago," he told Hotsheet. "It's going to go away as quickly as it came on."