Buresch was born the son of a merchant in Groß-Enzersdorf, Lower Austria, where he attended primary school (Volksschule).

During the 1920s and early 1930s he was a delegate to the National Council parliament (1920-1934), Landeshauptmann governor of Lower Austria (1922-1931 and again 1932-1933), and a chairman of the Christian-Social group.

Upon the collapse of the biggest Austrian bank Creditanstalt in May 1931, difficulties created by the Great Depression and the instability of the national currency, the First Republic found itself in political turmoil.

On 20 June 1931 Buresch was appointed Chancellor of Austria and finally managed to form a cabinet of Christian Social and German nationalist politicians, after unsuccessful attempts by his predecessors Otto Ender and Ignaz Seipel to cope with the crisis.

As the commercial crisis continued and domestic policies deteriorated after a failed Heimwehr putsch led by Walter Pfrimer, Buresch lost his German nationalist allies and went on to govern with a minority cabinet from January 1932.