Mayor Bill de Blasio sailed into office on the winds of a well-run campaign. Then he kept on campaigning, pressing for one overriding goal: a vast expansion of full-day prekindergarten and after-school programs, financed by an income tax on wealthier New Yorkers. Though the tax has always had only a whisper of a prayer of coming true — it needed approval in the State Legislature, and Gov. Andrew Cuomo and Senate Republicans were dead set against it — Mr. de Blasio pushed on anyway, giving no indication of having a Plan B.

This seemingly quixotic quest has just entered a new phase in Albany, where a budget is due on April 1. The Assembly, as many expected, last week embraced Mr. de Blasio’s pre-K tax, which would raise about $532 million a year for five years. Then the Senate proposed giving Mr. de Blasio even a little more than he was asking for — $540 million — although it rejected his tax as a way to pay for it.

These numbers aren’t real — in Albany nothing is, until the closed-door budget dealing is done — but they look pretty good for the mayor, and put him in the odd position of winning while losing. Though his tax seems as doomed as ever, the biggest question now looming over his pre-K initiative is not whether it will happen, but how much money it will get.

Now, as Mr. Cuomo said in a statement, “real discussions can begin.”

The next two weeks are where Mr. de Blasio can make the hard turn from campaigning to leadership. He has a formidable rival in Mr. Cuomo, who has spent months disparaging the mayor’s pre-K tax while offering his own “blank check” to expand full-day pre-K statewide. Mr. Cuomo has cast himself as the greater protector of New York’s 4-year-olds, though the amount he proposed in his budget — $100 million for next year for all school districts — isn’t even enough to get New York City’s pre-K program off the ground.