Seymour is likely to be re-elected in September as National has again told its supporters to vote for him in Epsom. But he is concerned that it could be harder to pass the bill under the next Parliament.
New Zealand First, which has risen in some political polls, wants a public referendum on euthanasia and could oppose his bill.
And some of National's socially liberal MPs in safe seats, including John Key and Maurice Williamson, have been replaced by more conservative candidates.
Seymour said his bill provides the best chance of a law change in New Zealand because National has ruled out changing the law and Labour says it is not a priority.
Recent opinion polls have shown that between 65 and 75 per cent of New Zealanders are in favour or medically-assisted dying.
Parliament's Health Committee completed a major inquiry on public attitudes to euthanasia last week, and did not recommend that the Government legalise euthanasia.
The committee's chair, Simon O'Connor, said the case had not been made for voluntary euthanasia regime in New Zealand, because there were widespread concerns that the elderly and disabled would be vulnerable if the law was changed.