Is Clinton barred from State job?

Pete Williams of NBC raised the question on MSNBC this afternoon: Is Hillary Clinton barred by the Constitution from accepting the post of secretary of state?

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.