But a Herald straw poll shows the vote is closer than he thinks.
A total of 33 MPs told the Herald they would definitely or probably support the bill to a select committee, and 27 said they definitely or probably would not. Another 37 MPs were undecided, and the rest did not say or did not respond. Seymour needs 60 votes for a majority.
Among the high-profile opponents is Prime Minister Bill English, a practising Catholic who has long opposed assisted dying. Deputy Prime Minister Paula Bennett was undecided, but said she was not definitely opposed.
One of the strongest voices against the bill was Deputy Speaker and National MP Chester Borrows.
"We have a horrific record on suicide and I think it sends a message that sometimes it is okay to top yourself," he said.
Leader of the Opposition Andrew Little has previously said he would support legalisation if it had appropriate safeguards.
Most Labour MPs supported the bill, including deputy leader Jacinda Ardern.
The Green Party has a formal policy of legalising euthanasia for terminal patients. Health spokeswoman Julie Anne Genter said Seymour's bill went further, and her caucus would need to discuss it before deciding its vote.
New Zealand First's policy is to hold referendums on conscience issues, and it is likely to oppose the bill unless Parliament agrees.
Maori Party co-leader Marama Fox said she could not support a law change.
"I've sat holding the hands of dying people over and over again so I have a good understanding of this and I've never once heard one of those people tell me they want to go early."
The campaign against the proposed law change looks set to be led by the Care Alliance, a lobby group whose members include the Salvation Army.
Care Alliance secretary Matthew Jansen said yesterday he looked forward to exposing the flaws in Seymour's bill.
"One thing we know from public polling is the more people learn about euthanasia, the less they like it. It is a death on demand bill."
Seymour acknowledged public fears about the issue, and said he had addressed many of them through a series of safeguards, including approval from two doctors, one of them independent from the patient.
"This is morally, democratically and legally the right thing for Parliament to do," he said.
The bill represents the best chance for voluntary euthanasia to be legalised in New Zealand.
A Parliamentary committee is separately considering a petition to legalise euthanasia, but National and Labour have ruled out making it a priority.
The inquiry was prompted by a petition that followed the death of Wellington lawyer Lecretia Seales, who unsuccessfully sought a High Court ruling that would have allowed her doctor to help her die without criminal prosecution.
Seales' husband Matt Vickers said yesterday she would be "over the moon" that Parliament was now debating the issue.
What does the bill do?
• Allows mentally competent New Zealand adults who have a terminal illness likely to end their life within six months, or have a grievous and irremediable medical condition, the choice to ask a doctor to help end their life at the time of their choosing.
• The patient must have the ability to understand the nature and consequences of assisted dying.
• A new process will require two medical practitioners to be satisfied a person meets the required criteria. The second would be independent of the patient and initial doctor.
• The Director-General of Health would establish a group of medical practitioners who will maintain a register of health professionals willing to participate in assisted dying.
• To be eligible, a person must be aged 18 years or over and be a New Zealand citizen or resident.
