I found a Russian translation in a Soviet edition of his poetry («Избранная лирика», 1981). The poem is from his 1945 collection Na zlobu dňa (On the topic of the day). The text is supplied with the place and date: Nitra, 17 July 1929. The date is corroborated by this online publication. Slovak Wikipedia says Jesenský held the office of grand prefect (veľkožupan) in Nitra and was active in political and social life.
The poem talks about empty promises of political parties, so this might imply the 1929 Czechoslovak parliamentary election (held on 27 October 1929). However, Jesenský was critical of Czechoslovakia’s political scene in his other works, such as the novel The Democrats, written in the 1930s. Sarah Hinlicky Wilson writes:
It helps to remember that Czechoslovakia (as it was at the time) was
the only Eastern Bloc country with experience of democracy before
Communism; but at the time of the story, it was little more than
fifteen years into democracy and they were still figuring it out. It
appears that Jesenský thought the competition and mutual slander were
indecent and degrading, working against national unity instead of in
its favor. Not to mention the very personal motivations he perceived
for this, that, or the other politician to adopt certain views or
campaign for a certain party.
Hinlicky Wilson adds that the first section of the novel, in English translation, is available online (with introduction and commentary), suggesting possibilities for further research.