I'm assuming you're talking about "within the United States." Because, otherwise, the answer is probably the Cambridge Five, who ended up in some of the upper reaches of the British Government including

• Kim Philby -- 1st Secretary to the British Embassy to the United States and chief British intelligence representative to the United States.

• Donald Maclean -- Secretary of the Combined Policy Committee on atomic energy matters. Later he was appointed head of Chancery for the British embassy in Cairo and took a key role in planning to secure the region for the West should war break out with the USSR.

• Guy Burgess -- Assistant to the British Minister of State in the Foreign Office. He was also eventually posted to the UK embassy to Washington DC.

• Sir Anthony Blunt -- Passed information from the codebreaking efforts at Bletchly Park to the Soviets. Also served as the Surveyor of the Queen's (King's) Pictures.

Not exactly 'federal' but Jon Anthony Walker was a spy for the soviets. He was a Navy CWO and an advisor for submarine communications in the Atlantic theater who passed incredibly sensitive Navy encryption and cypher's to the soviets, leading to the American navy unknowingly being completely susceptible to Soviet communication intercepts during Naval war games and general exercises. Moreover, he passed on knowledge of highly secret Naval technology, leading the Soviets to countering American submarine detection. Walker's activities gave the Soviets some of the greatest and most significant military intelligence during the latter half of the Cold War.

Interestingly, by all accounts Walker had no real allegiance to the Soviet Union, rather he did all this purely for the massive amounts of money the Soviets offered him for the information. There are a few more 'bigger' spies, Such as Aldrich Ames and Robert Hanseesn, but In my personal opinion, Walker's story is by far the most interesting if you want to look into the subject further.

Sources:

Hoffman, David E., The dead hand: the untold story of the Cold War arms race and its dangerous legacy (New York, 2009)

Aldrich, Richard, Black door: spies, secret intelligence and british prime ministers (2016)

Alger Hiss was the Director of the Office of Special Political Affairs in the State Department in the critical final phases of WWII, and was a key aide at the Yalta Conference where the fate of Eastern Europe was being settled. He was also the Executive Director of the Dumbarton Oaks Conference that was the planning conference for the United Nations. The Venona decrypts indicate that he actually was decorated by the Soviet government. He later was convicted of perjury for his denial of being a Soviet spy. Here is a CIA summary of his case.

Harry Dexter White was a senior Treasury Department official who dominated the Bretton Woods Conference as the US representative in 1944, which planned the postwar international economic institutions such as the IMF and the World Bank. He also appears in Venona.