But the opponents’ challenge is daunting: The deal reached between Gov. Andrew M. Cuomo, Mayor Bill de Blasio and Amazon was explicitly constructed to minimize the ability of local politicians to block it. The company would not agree to come to New York City, Mr. de Blasio said, unless it could be assured it would not have to go through the lengthy process of approvals that would give the City Council veto power.

The closed-door deal to avoid local review has angered many Council members and state legislators, some of whom appeared at Wednesday’s rally.

“Why did they usurp the ability of the Council to do its job?” asked a newly elected assemblywoman, Catalina Cruz, who represents the nearby Queens neighborhoods of Jackson Heights, Corona and Elmhurst. “Because it’s not good for our community.”

But what can opponents actually do to stop it?