The Government is confident peers will be "constructive" over key Brexit legislation as a marathon two-day debate began.
Lords Leader Baroness Evans of Bowes Park said she did not share concerns that peers will ignore the referendum or use the European Union (Withdrawal) Bill to frustrate the Brexit process.
She added she expects deliberations to be "very challenging" but noted they have a duty to "deliver on the will" of the British people.
For Labour, shadow Lords leader Baroness Smith of Basildon stressed the need to amend the legislation to provide greater clarity.
She also mocked the Prime Minister for arguing for a "clean bill", as if somehow amendments made "legislation dirty and impure".
Labour former transport secretary Lord Adonis also proposed a rare motion of regret that the Bill, which aims to transfer European law into UK law, did not provide for a second referendum on the terms of the final Brexit deal.
Almost 190 peers are listed to speak over the two days of second reading, where the principle of the Bill will be considered.
Opening the debate, Lady Evans said the Government was making "good progress" with the Scottish and Welsh administrations on how devolved powers were treated in the Bill.
Ministers have previously committed to bringing forward amendments on this issue in the Lords.
She went on: "Not for the first time, there has been much speculation about what might be expected from (the Lords), as we consider this Bill.
"Some suggest that this House will ignore the referendum or attempt to use the Bill to frustrate the Brexit process.
"I don't share those concerns. I am keenly aware of the collective sense of responsibility felt across this House to our important constitutional role and I am confident noble Lords will take a constructive approach to our deliberations.
"I am also very confident that those deliberations will be thorough and very challenging, which is exactly as it should be."
Labour's Lady Smith said all peers want to avoid this becoming a "fiendishly complex" process that weakens both parliamentary sovereignty and legal protections.
She added: "The time for slick soundbites to pacify extremists has long since gone.
"Instead of vague superficial statements of a 'Global Britain', 'Brexit means Brexit' and now the appalling 'Buccaneering Brexit', we have to deal with the reality and the nitty gritty of the detail. That is the test for this Bill and the Government."
Turning to Lord Adonis' amendment, she said: "Although a further referendum is not something I am attracted to at this stage for a number of reasons, I really don't think it is an appropriate amendment for second reading or that it fits into this Bill, given the nature of the issues before us.
"Should he put it to a vote tomorrow, I don't intend to vote."
Lord Adonis earlier said the interests of the public as a whole "do not lie in making Britain poorer".
He added: "They do not lie in undermining the Good Friday Agreement. They do not lie in diminishing trade and our people's right to live and work across Europe.
"They do not lie in scapegoating Europe and foreigners for the social challenges that we face and they emphatically do not lie in weakening our solidarity with Germany and France and the other democracies of Europe in standing up to Vladimir Putin and others who now and in the future threaten our borders, our lives and our values."