Will a COL increase Prevent Clinton from becoming Sec. of State?

A Republican story line that is getting noise is the notion that Hillary Clinton is Constitutionally ineligible to be Secretary of State because the position received a cost of living salary increase during her term in the Senate.

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; ~ U.S. Constitution - Article I, Section 6, Clause 2

A cursory review found six prior Secretary of States who fell into Clinton's situation. In descending order they were Edmund Muskie, Philander Knox, James G. Blaine, Daniel Webster (twice), James Buchanan, and Martin Van Buren. I am sure there are several additional examples with other cabinet posts.

Both Webster and Van Buren resigned from the Senate several weeks before being nominated for the cabinet position. I'm no Constitutional law professor and I have no intention of doing the historical digging necessary to confirm this, but I suspect way back in the early 19th century, when the Constitution was still new, resigning from the Senate prior to being nominated was sufficient to meet this clause's requirement.