The Senate's 17-13 vote Tuesday followed a Judiciary Committee recommendation last week to kill the bill. Debate on preliminary passage comes Wednesday.
Tuesday's vote followed an impassioned day-long debate in which several senators spoke of the deaths of their own family members.
The Senate chamber included spectators on both sides of the issue.
Supporters say they want to increase choices for people trying to manage their final days. Opponents said they fear people may end up being coerced into ending their lives and that doctors should not be in the role of helping people die.
Supporters call the bill, "end-of-life choices" while critics call "physician-assisted suicide."