And it's not even really a debatable point.
Article I, § 6.2 of the United States Constitution:
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."Emoluments" is deadwhiteguyese for "pay". The point being to keep Congresscritters from creating cushy jobs in the bureaucracy and having themselves appointed thereto.
President Bush, in keeping with the cost of living increases lavished for no particular reason on government officials, raised the emoluments of the Secretary of State in January, 2008, which is during the current Senate term of Hillary Clinton.
The good and wise Professor Volokh (w/t) thinks that it would be enough to lower the pay for the secretarial job back to January, 2007 levels.
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