Two Assembly members and other advocates of letting the terminally ill end their lives say the proposed law would limit suffering and has safeguards to prevent mistakes and abuse.
Opponents, who on Tuesday included the Senate majority leader, aren't convinced.
Bills pending in the Assembly and Senate since last year are getting a new push in Albany.
Assembly member Amy Paulin, a Westchester Democrat whose sister died painfully and slowly from cancer, says people in that situation should be able to choose a calm, peaceful and dignified end at their chosen time.
Assembly Health Committee Chairman Richard Gottfried, a Manhattan Democrat, agrees.
John Flanagan, the Long Island Republican who leads the Senate, says his immediate feeling is that he doesn't like it, adding any action should be approached with caution.