Article 2, Section 2, Paragraph 2 of the US Constitution:
"He shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, provided two thirds of the Senators present concur;"
Senators are members of the upper chamber of the legislature, which is 1/3 of the US government (executive and judicial branches being the other 2/3.) The letter was fudgingg asinine, but to suggest that, as US Senators, they cannot involve themselves in foreign affairs is simply an indefensible position. They -are- the US government, just as much as any other elected federal office holder is (like, say, a President.)
P.S. - Notice that says "He shall..." We sure were sexist back then.
P.P.S. - No, I'm not really back. This is a drive-by posting.