As many noted, probably a majority of the government faction are shomer shabbat.
So, now comes the challenge – as the whole world looks with a magnifying glass at Am Isroel – will they see am kadosh venavon or will they see infighting and hillul Hashem? One of the haverei knesset is quoted as saying to a loser: “we will treat you fairly, we are not animals like you”, which is encouraging sans the comparison…
So, if davening for election results or skipping tachanun may or may not be appropriate, davening for the new government to be wise and honorable is certainly appropriate.