Lord Falconer, who is leading the bill’s passage through the upper chamber, put forward the proposal for extra time to allow peers to consider the legislation.
Speaking during a debate on the motion, which passed without a vote, he warned that if peers failed to reach a conclusion “it would significantly damage the reputation” of the House of Lords.
Former Lord Justice of Appeal Baroness Butler-Sloss also warned the reputation of the House was “at stake”
Supporting the proposals for more time, she told peers: “I don’t like the Bill, but we have it, and we have to deal with it.”
However, Conservative peer Lord Shinkwin, who has rare brittle bone disease osteogenesis imperfecta, argued that peers had already “been generous with our time”.
“We can only ever work with what we have been given, the volume of amendments, and the time taken to consider them, therefore, reflect the quality or lack thereof of the bill that was sent to us,” he said.
“If any bill is so poorly drafted and so unsafe, surely the question is not so much whether the bill deserves more time as whether yet more time could transform it.”
A source close to peers concerned about the bill said: “Supporters of assisted dying seem determined to keep complaining about the process in the Lords rather than engaging with significant failings in the bill.”
They added that the motion was not accompanied by “any acknowledgement of the scale of the problems identified by Lords committees and external experts or of what amendments Lord Falconer is willing to accept to address those problems”.
The government’s chief whip in the Lords, Lord Kennedy, said he would look to hold “urgent discussions” early next week “to seek to find a way forward to deliver on what the House has just agreed”.