Inside the budget deal are some critical practical — and political — demands from Mr. Cuomo.

Tax experts had viewed Mr. Cuomo’s proposed workarounds with skepticism, warning that many of the ideas were purely academic and had never been tried in practice. Others worried that the payroll tax workaround would be unpopular with New Yorkers, as it would result in lower gross pay, even if their take-home pay would ultimately remain the same.

Still, the new tax policies — while limited — will allow the governor a credible argument that he is fighting for New York in the face of the White House and Republicans in Washington.

The governor also secured $250 million in new funding for the troubled New York City Housing Authority, making good on a promise he had loudly and repeatedly declared over the past few weeks. After three visits to public housing projects, he vowed not to sign the budget unless it included a “real remedy” for repairs at Nycha, where residents have faulted Mr. Cuomo’s intraparty rival, Mayor Bill de Blasio, for deteriorating conditions.

On an issue of vital local importance, the budget also includes $26.7 billion in school funding — a higher figure than either Mr. Cuomo or the Republican-controlled Senate had proposed in their own preliminary budgets.

Mr. Cuomo is facing particular pressure to burnish his progressive credentials: The actress and education advocate Cynthia Nixon, who is challenging him for the Democratic nomination for governor, has blasted him for what she called his “massive disinvestment” in schools and in other areas that affect black and Hispanic residents.

On that account, Friday was a mixed success for the governor, with pledges to introduce early voting, end cash bail for low-level offenses and codify the Supreme Court ruling that legalized abortion all failing to make it into the final budget deal.