Why should the ultimatum Carlo Calenda gives to Enrico Letta of the PD party be of any consequence to the Draghi administration?

It’s a situation a bit complicated. There’s been the Morisi scandal on the Lega Nord part (https://en.wikipedia.org/wiki/Lega_Nord), the conviction in the first instance of the Mayor of Riace Domenico Lucano to 13 years. Then, there’s been the Fanpage inquiry to Fratelli d’Italia internal affairs (https://en.wikipedia.org/wiki/Brothers_of_Italy), which resulted Carlo Fidanza, also called the Black Baron, investigated for illicit financing, and exposed him and many others as fascist. Now, what does it have to do with the question? Because in Italy, maybe some of you heard, there have been quite recently the administrative elections in many municipalities, including Rome. Now, Calenda, leader of the Azione party, (https://en.wikipedia.org/wiki/Action_(Italy)) has been a candidate of the elections in the capital, and earned in said elections a consensus of 20%. Now, he and Gualtieri are going to the second ballot. The point is, he gave an ultimatum to Letta: either he stops supporting Conte and the Movimento 5 Stelle (https://en.wikipedia.org/wiki/Five_Star_Movement), or Calenda, basically, won’t support him. The point of all this discussion is, there are some who say Calenda’s ultimatum has an impact on the Italian administration of Draghi. Why does what Calenda says about his support in the elections in Rome have any impact on the Draghi executive? He chose not to be in the Parliament (afaik), just in the capital.