I forgot to answer your question specifically:
If you work at McDonalds AND you give McDonalds a Social Security number, making mcdonalds your witholding agent, then YES you are acting as an agent of government. BECAUSE, they are borrowing a chunk of your money and in return they will (eventually) pay you social security retirement benefits.
IF you're in D.C., Congress could literally take 100% of your pay as a direct tax if they wanted to. WHY? because the direct tax clause of the Constitution DOES NOT APPLY in D.C. or other territories, AND congress has "absolute legislative jurisdiction" in D.C. "absolute" is not a word the courts use often.
“It is clear that Congress, as a legislative body, exercise two species of legislative power: the one, limited as to its objects, but extending all over the Union: the other, an absolute, exclusive legislative power over the District of Columbia. The preliminary inquiry in the case now before the Court, is, by virtue of which of these authorities was the law in question passed?”
[Cohens v. Virginia, 19 U.S. 264, 6 Wheat. 265; 5 L.Ed. 257 (1821)]
EVERY TIME you use that S.S. number (or any other federal device) you are acting as Federal Personnel, and thereby part of the Government, and you know what the Constitution says about government:
Article 1, Section 8 clause 14 states:
[The Congress shall have Power To] make Rules for the Government and Regulation of the land and naval Forces;