Is Hillary's appointment unconstitutional?

Could Hillary Clinton's appointment be unconstitutional? Ben Smith thinks it could be:

With Hillary's expected appointment tomorrow comes a round of buzz about "emoluments" and specifically the question of whether, under a fairly straightforward reading of the Constitution, her appointment isn't constitutional.

At issue is Article I, Section 6, which 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." That is, if the Cabinet, or other, post got a pay hike during the term of the senator, the senator couldn't take the job. During Clinton's Senate term, Bush raised the Cabinet's pay.

And there are serious lawyers who see this, legally speaking, as a real obstacle.

However, there have been other occasions when this has arisen - the appointment of Llyod Bentsen as Treasury Secretary for instance. The solution is to cut the salary of the incoming Senator/Secretary.