[5] As a youth, he "decided he wanted to become a lawyer after hearing a radio speech by the late Sen. Dennis Chávez".
[3][5][7] He worked as a law clerk in the New Mexico Highway Department from 1964 to 1965, and as an assistant district attorney in Santa Fe from 1965 to 1966, thereafter entering private practice in Albuquerque until 1972.
[4] As a district court judge, Baca "was known for being tough on criminals", being given the nickname "Maximum Joe" for imposing long sentences.
[6] In 1988, Baca received the Democratic nomination for a seat on the state supreme court, and was elected to an eight-year term that November, handily defeating Republican opponent Ken McDaniel.
[9] In 1994, the Hispanic National Bar Association recommended Baca as a potential nominee for the seat on the Supreme Court of the United States vacated by the retirement of Justice Harry Blackmun.
[18] Baca indicated that he would continue working in mediation and arbitration, for which he had attended a program in California the previous year.