Conservative MPs who voted to support the Trudeau government's physician-assisted-dying bill as it makes its way to committee for further study say they did so on the word of their constituents – with some even pushing for more people to be eligible than the Liberal legislation currently allows.

Some 20 Tories stood up to support the federal government's Bill C-14 at a second-reading vote on Wednesday, a show of faith from across the Commons – even as many say they would like to see changes to the bill, which faces criticism on all sides and a looming June 6 deadline from the Supreme Court of Canada.

The bill will now be studied at a parliamentary committee, where amendments can be made, before it returns to the House of Commons for another vote and then on to the Senate, which is already hearing from witnesses to save time.

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Conservative MP Ron Liepert, who voted in favour of the bill, said his Calgary-area riding conducted numerous surveys on the topic and the results were clear. "Pretty consistent from Day 1 was a large support for the concept of medical assistance in dying," he said in an interview.

Another Conservative MP, Cathy McLeod, also canvassed her B.C. constituents and estimates that up to 70 per cent of people are in favour of physician-assisted dying.

"If I had a family member with ALS [amyotrophic lateral sclerosis] and this was the choice that they wanted, to maybe be in their own bed … looking at mountains with their favourite music, as opposed to something like palliative sedation, would I be able to deny their request for an escape from this intolerable pain and suffering?" said the former nurse, who represents a riding in Kamloops.

Still, Ms. McLeod said she wants more safeguards, such as a psychiatric and social-work assessment, or a judicial review before the procedure – and she'll wait to make up her mind once she sees the final bill.

Other Tories who supported the bill at second reading want to see additional conscience protections for physicians who refuse to participate, more money for palliative care and more clarity around protecting those with mental illness.

But over all, they agree with the concept laid out in the February, 2015, Supreme Court decision that said consenting adults with a "grievous and irremediable medical condition" who are suffering intolerably have the right to end their lives with the help of a doctor.

"By my deepest principles … I cannot oppose this," Quebec Conservative MP Alupa Clarke said.

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For some Tories, the government's response to the high court ruling does not go far enough. "It's a grossly deficient bill," said Peter Kent, the MP for Thornhill, north of Toronto, who nevertheless supported it at second reading.

"The legislation falls far short of what the Supreme Court directed. And it also doesn't include dementia and Alzheimer's."

In Mr. Kent's interpretation of the bill, which stipulates a patient's "natural death must be reasonably foreseeable," only terminally ill cancer patients would qualify for the procedure, and he wants it expanded to include non-fatal but degenerative diseases such as multiple sclerosis.

But he said he chose to support the legislation because "it's a very tiny first step" toward giving seriously ill Canadians a choice at the end of their lives – a conclusion he came to after meeting many different people in his community.

"Most of them are satisfied when I say that I believe this whole thing comes down to a matter of individual, competent choice," he said.

Mr. Liepert, too, would have liked to see the bill expanded to include requests made in advance for those with mentally degenerative conditions such as Alzheimer's. "I personally believe advanced consent needs to be considered, and I would support advanced consent," he said.

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Meanwhile, the lead lawyer who fought for the right to assisted dying at the Supreme Court said Thursday that the government's bill is unconstitutional because it focuses primarily on those who are at the end of their lives.

"I would rather see this bill die and there be no legislation," lawyer Joseph Arvay told a Senate committee.