[What you need to know to start your day: Get New York Today in your inbox.]

After announcing a deal to bring an Amazon headquarters to New York, Gov. Andrew M. Cuomo and Mayor Bill de Blasio might have expected to be taking a victory lap, having beat out hundreds of other elected leaders from around the country who also wanted to boast about new jobs in their region.

Instead, they have spent the last week doing damage control. So far, it isn’t working.

On Tuesday, two of the most outspoken critics of the deal, State Senator Michael Gianaris and City Councilman Jimmy Van Bramer, said that state officials had invited them to join an as-yet-unannounced community advisory committee that would provide input on planning but would have no ultimate veto.

They refused. “They are trying very hard to move from announcement to implementation, and we do not accept the announcement,” Mr. Gianaris said of how he believes the state, the city and Amazon moved to complete the deal. “That’s why we’re not participating in this charade.”

Mr. Van Bramer took a similar view. “I think it’s going to help get us what we want,” he said of his refusal to join the committee. “Because what we want is to stop this bad deal.”