A member of the Republican Party, he was the United States Ambassador to Uruguay from 2006 to 2009 under President George W.

[13] His term also coincided with a period of tension over alleged CIA involvement in the assassination of Cecilia Fontana de Héber.

Cecilia Fontana was from a prominent family — spouse of a National Party leader, mother of a National Party politician who was appointed to serve in the government of President of Uruguay Luis Alberto Lacalle Pou in 2020 and sister-in-law to a President of Uruguay who served in the 1960s — and had died in 1978 after drinking from a bottle of poisoned wine.

Citing communications obtained from the 2010 United States diplomatic cables leak, El País reported that Baxter delivered a request for declassification of documents related to the matter from Uruguayan President Tabaré Vázquez to George W. Bush in April 2008.

The paper further reported that Baxter had pushed back by bringing up the killing of Dan Mitrione and expressed the hope "that the poisoned wine case has definitely been laid to rest".