Judicial Watch says the Constitution prohibits a member of Congress from resigning to take a better-paying job in the Executive Branch in certain circumstances, which means Clinton will have to remain the junior senator from New York.

Judicial Watch said the rule is known as the Ineligibility Clause and is ironclad despite moves by past presidents to get around it by lowering the pay of a specific Cabinet post to fill it with a sitting senator or congressman.

The tactic used by Presidents Clinton and Nixon is known as "The Saxbe Fix" and Judicial Watch considers it illegal. The Ineligibility Clause, the group said in a written statement Thursday, specifically bars lawmakers from Cabinet posts if the pay level was increased while they were in office.

"The Saxbe Fix" may reduce the salary of secretary of state to previous levels, but it does not affect what is a clear constitutional prohibition," the statement said. "It cannot change the fact that the salary had been increased while Senator Clinton served in Congress."