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; and no Person holding any Office under the United States, shall be a Member of either House during his Continuance in Office.
The argument goes: Hillary Clinton served in the Senate during a period in which the compensation for the Secretary of State was increased by way of executive order, therefore she is ineligible to assume that position.
I read the clause to disqualify her from the office until 2012 (the ‘Time for which [s]he was elected’.) The only necessary condition for the clause is that emoluments ‘have been increased’ during the time. Most people can agree on this point but there is a small contingency- likely in the single digits- that believes that the Senate may simply lower the wage to pre-election levels for the potential nominee.
The most common fix for the Emoluments Clause is the so-called ‘Saxbe Fix’ although it was used long before Richard Nixon appointed Senator Saxbe to Attorney General in 1973. President Taft had used it in 1909 and its Constitutionality has been debated by subsequent administrations. Rumor has it that because the Reagan administration decided that the Saxbe Fix was unconstitutional, they avoided appointing Sen. Orrin Hatch to fill the seat left by the retiring Justice Lewis Powell. The administration would later appoint Anthony Kennedy to fill the seat after the failed nominations of Robert Bork and Douglas Ginsburg.
DailyKos has interesting analysis from Madison’s notes at the Constitutional Convention. I tend to think the Saxbe Fix conforms quite reasonably to the intent of the Emoluments Clause but does not stand up to what the text of the clause actually reads. Unfortunately then, I would consider the appointment of Hillary Clinton to Secretary of State (before 2012) to be unconstitutional.