In theory, they had nothing to worry about, because the governor had given his word in January, shortly after his State of the State address, that the vast cuts to Medicaid and CUNY in his executive budget “won’t cost New York City a penny.” Which is hard to believe, since Mr. Cuomo has been insisting, in various and shifting ways, that the city will have to fork over hundreds of millions of dollars in spending that the state seemed intent on shrugging off.

In Albany, no budget is done until it’s done, and it’s hard to predict where the deal-making ends up. But the starting point, the executive budget Mr. Cuomo released in January, was colossally bad for New York City. It cut $485 million in state funds for CUNY, based on the administration’s false insistence that the university’s administrative costs are “bloated.” (Independent analysis shows that the CUNY system spends less on administration than most of its peers.)

The budget also shifted to the city — and no other municipality in the state — some of the rising costs of Medicaid, reneging on an obligation the state had assumed in 2012. City officials estimate the state Medicaid cuts would cost city taxpayers $300 million in the 2017 fiscal year, rise to $1 billion a year in 2022, and keep climbing.

City officials were recently told that the CUNY cuts were off the table, but they are waiting for the final deal, and watching for signs of other budget punishment: One troubling proposal was for the state to help itself to $200 million in city sales taxes each year, for three years.

Democrats in the Assembly have been pushing back at the moving targets — like Mr. Cuomo’s destructive Medicaid plan, which morphed this week into a proposal for $250 million in statewide Medicaid “savings,” a dubious search for “efficiencies” that would hit hard in New York City, where most Medicaid patients are.