The Christian charity CARE has urged MPs to reject the proposal, while the Bishop of Buckingham has supported a change in the law.
It's currently illegal to help someone end their life.
The Assisted Dying Bill would allow a terminally ill person with six months or less to live, to ask to be prescribed lethal drugs if two doctors agree they have a clear and settled intention to die. A High Court judge would have to review each case.
The Assisted Dying Bill receives it second reading on September 11, which will include a vote on whether it should reach the next stage of passing a law or not.
Premier's Political Editor Martyn Eden has said it could be another six months before a potential bill on assisted dying becomes law.
He also said four similar bills on assisted dying have been rejected within the last decade.
Dan Boucher, the Director of Parliamentary Affairs for the Christian charity CARE, told Premier's News Hour: "Doctors are very much opposed to it.
"The BMJ had a poll... and they asked the question whether this new provision that they've inserted in the bill to say a judge must give consent would protect the vulnerable, 65 percent said 'no, it wouldn't'.
"Consider this: it costs five pounds to have a drink of barbiturates to end your life, it costs about three thousand pounds to keep you in a hospice for a week...
"It would be very naive to think that if you introduce this legislation it wouldn't generate significant pressure on very vulnerable people."
The Bishop of Buckingham, Rt Revd Alan Wilson, told Premier's News Hour: "Very, very few people in countries where such laws operate actually use it, and I'm sure that's right - I don't want more people to use it. But the fact that it's there can give them a sense of autonomy and dignity in the face of terminal disease.
"If people turn out to live longer than their prognosis, praise the Lord! Nobody's trying to kill anyone here, that's absolutely delightful. It's the fact they have a possible way out if things did not work out well for them, and that they have some measure of autonomy about that."
Listen to the full debate on Premier's News Hour with Des Busteed:
