Some MPs have also changed their stance, by supporting the bill. Minister Chris Bryant is understood to be backing it, having abstained in November. Labour MP Jack Abbott, who voted against last November, is also now likely to vote in favour.
Others who were hesitantly supportive are now more firmly in favour.
Liz Saville Roberts, the leader of Plaid Cymru at Westminster, said she was initially concerned but supported the principle of assisted dying.
"I think the safeguards have got stronger," she said. "They have been improved through the bill committee and through the evidence that we heard."
One of the changes made as the bill was scrutinised was allowing Senedd members a vote on whether it will apply in Wales.