Critics said the assisted-dying bill could still be voted on.
Conservative MP Danny Kruger hoped it would be dropped because too many MPs were uneasy about the disputed legislation.
The proposed law passed the first hurdle after representatives voted 330 to 275 in its second reading on Friday.
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But Krueger said: “This is not the end, this is just the beginning.”
He said it could still be voted down on third reading if MPs were not satisfied with the improvements next year.
He added: “There is a strong feeling that it is not over yet, which is very encouraging.
“We're talking about a few dozen people who can change their votes if they're not satisfied with the final look of the bill. It's not over at all, and that's what the other side is saying.”
Kruger said a lot of safeguards were needed, adding: “The fact that a doctor can suggest euthanasia for someone who doesn't want it, right down to the fact that it's the judge who runs the proceedings in secrecy without any investigation into any coercion.” Or pressure on the patient.”
One of the representatives said that she had been crying all week and was crying in the hall because of some speeches.
Another added: “It's been an emotional rollercoaster.”
Prime Minister Keir Starmer was among those who backed the plan that would allow terminally ill adults with a life expectancy of less than six months to end their lives.
Some representatives indicated during the discussion that they might waive their support if they were not convinced by the guarantees.
MPs on both sides have called for improvements to palliative care.
Some hospices will ask for a conscientious objection to assisted dying, Charity Hospice UK said.
Senior doctors said the struggling palliative care system should be an immediate priority for the government.
The Society for Palliative Medicine says there is a risk that funding needed to pay for doctors and courts to oversee assisted dying will divert money away from care for the dying.
“The UK is often seen as having the best palliative care in the world – but that is not the case anymore. We are not getting the funding we need,” Dr Sarah Cox told the BBC.
The bill will then move to the committee stage, where MPs can submit amendments, before facing a vote in the Commons and Lords.
No change in the law will be agreed upon until next year at the earliest.
Kim Ledbetter, who led the bill, said it will likely take another two years from then until assisted dying is implemented.
