“We are seeing elected officials turn back because of fear-mongering,” said Akeem Browder, the brother of Kalief Browder, a Bronx teenager whose long incarceration on Rikers Island and subsequent suicide galvanized the push for reform. “That’s cowardice. It’s atrocious.”

Opponents of cash bail have long argued that it criminalizes poverty, tilting the justice system in favor of wealthy defendants, and can result in collateral damage as the accused lose jobs, apartments and relationships while incarcerated for minor offenses.

New York is among several solidly Democratic states, like California and Illinois, that have limited the use of bail, though legislatures in more Republican states like Texas and Alaska have also embraced reforms. But unlike New Jersey, which passed reforms in 2014, New York did not give state judges the discretion to consider whether a person posed a threat to public safety in deciding whether to hold them.

Mr. Cuomo’s original bail reform proposal had included a tool that would allow judges to assess the risk to public safety by granting someone bail, but legislators did not include it in the bill they passed last year.

Some of the proposals being floated by lawmakers would grant judges that discretion, a change that has been supported by Mayor Bill de Blasio, a reform-minded Democrat who cautioned that any change should include a “very precise definition of dangerousness” that would not be “overused.”

The New York City police commissioner, Dermot F. Shea, has also argued that judges should have greater power to hold potentially dangerous defendants. The state attorney general, Letitia James, a Democrat, has suggested that the new laws be revisited but declined to say which changes she supported.

Mr. Cuomo’s aides declined to say on Tuesday whether the governor planned to address bail in his State of the State speech on Wednesday, but Democrats in suburban swing districts seemed eager to make changes to the bill.