ROME — For once, Prime Minister Matteo Renzi doesn’t seem to be in a hurry.

A day after Italians overwhelmingly rejected a constitutional overhaul on which he had staked his tenure, Mr. Renzi, 41, made a somber visit on Monday evening to the Quirinal, once home to popes and now the President of the Italian Republic, to formally tender his resignation. The president, Sergio Mattarella, asked him to postpone for a few days while his government finished a budget. Mr. Renzi, usually in a rush, agreed.

For Italians, who have seen 63 governments in 70 years, Monday’s resignation made for a ritual as familiar as the morning espresso, even as the stakes seemed far higher this time. The immediate question is whether the president, usually a ceremonial figure, would form a caretaker government staffed with technocrats. Or convince rival political parties to form a coalition government. Or call for new elections in 2017.

Elections might be most satisfying for a restive public, except that an electoral law approved last year is under court review and may now be obsolete after Sunday’s referendum.

For Italians who keep insisting they are hungry for change, Monday’s vote had the effect of ushering in an Italian Groundhog Day.