There is an excellent review of the situation here, by the Australian born, Italian citizen, head of the Brussels managing editor of MLex, James Panichi.
The Italian constitution vests significant powers in the president and President Mattarella is a very experienced politician who entered politics when his brother, at the time President of Sicily was assassinated by the mafia. Asked then to clean up the Sicilian branch of the Christian Democratic Party (DC). He was a member of the left in the DC, a concept difficult for those coming from countries where a catholic party would be expected to be deeply conservative. But the Democristiani were working in a different kind of world, where it as the confessional party contained within itself everyone from monarchists, fascists, conservatives to socialists and anarchists. The old DC regularly securing 40% of the vote to the Communist Party's 30%. Mattarella's faction favoured the 'apertura alla sinistra', opening to the left, and dealing with the communist party. He seems held in warm regard. He has told Renzi to stay in his seat and sort out budget and electoral laws. Mattarella is not rolling over for the right and populists calling for an election straight away.
For non-Australians seeking the meaning of the "Renzi’s Keatingesque strut" this is a reference to the wonder-modernist spit-on-fools former Australian Prime Minister Paul Keating, who also took on too many people at once, including a conservative electorate.