He was the Prime Minister of Denmark from 15 February 1968 until 9 October 1971. He was preceded and succeeded by the Social Democratic leader of that time, Jens Otto Krag. 1948-1951 Baunsgaard had been chairman of The Social Liberal Youth of Denmark.
In 1957 he became an Member of Parliament. By 1968 Baunsgaard"s party had been a frequent coalition partner of the Social Democrats for the last 15 years.
However, after the 1968 elections, he abandoned the Social Democrats and formed a centre-right coalition with the Conservative Party and the Liberal Venstre. The three parties held a clear majority of seats in the parliament.
In spite of this, they utterly failed to tackle the growing problems of the welfare state and rein in public spending. As a result, taxation skyrocketed.
In the social sphere the government was one of the most radical thus far seen in Denmark, abolishing censorship of pornography and legalising abortion.
However, in doing so they alienated sufficient numbers of core supporters to lose the 1971 election, which brought the Social Democrats back to power. Baunsgaard is often credited with being the first major Danish politician to truly embrace television as the main media for communication with the voters. He managed to connect with the voters, and was consistently rated as the most trustworthy politician from the mid-1960s to the early 1970s.
However his weak leadership of the government damaged his reputation.
Baunsgaard was the main architect behind Nordek, a proposed organization for Nordic economic cooperation somewhat similar to the European Economic Community (European Economic Community). The idea was embraced by both Sweden, Norway, and Iceland, but ultimately failed since Finland did not join due to its relationship with the Soviet Union, and Denmark joined the European Economic Community.