Article One, Section Six of the U.S. Constitution says:
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.
Essentially, you cannot take a job if the salary was increased during your current congressional term. And the salary for cabinet officials has gone up in the past year. Even if it is lowered back down, constitutional scholars say that may not be enough to fix the problem.
The question is whether this would be an issue at confirmation - if Clinton is nominated to the post - and who would raise it. Senators traditionally grant their colleagues some deference and it could be considered politics at its worst if Republicans try to block her nomination with this argument. But senators may be loathe to vote for something scholars tell them is unconstitutional.
That being said, this development may make Obama, or Clinton, think twice about the appointment.