Former Tory chancellor Lord Lamont has said it is the "duty" of Remain supporters not to undermine the government over Brexit.
Lord Lamont urged peers not to attempt to add conditions to the government's Brexit bill as it passed through the Lords.
But another ex-chancellor, Labour's Lord Darling, said the government should not get a "blank cheque".
Peers gave an unopposed second reading to the draft legislation.
More than 180 members spoke over the course of the two day debate, which lasted nearly 20 hours.
Urging peers to leave the bill unamended, Lord Lamont, who backed a Leave vote in June's referendum, said the views of the Remain side should be taken into account - and added: "But equally I believe that those who voted to Remain have a duty not to undermine the government's negotiating position."
But Lord Darling told peers: "I do not accept this argument that from now on those of us on the Remain side should sit back and say nothing and simply give the government a blank cheque to proceed."
He said this was impossible with so many "unanswered questions".
Liberal Democrat Baroness Kramer said voters should have "the final word" on the Brexit deal in a referendum.
MPs have already backed the proposed law, authorising Mrs May to inform the EU of the UK's intention to leave.
Although there was no formal vote on Tuesday, opposition peers are seeking to amend the bill at a later date to guarantee the rights of EU citizens in Britain and the role of Parliament in scrutinising the process.
As the government does not have a majority in the Lords, it is vulnerable to being outvoted if opposition peers - including Labour's 202 and the 102 Lib Dems - join forces. Much will hinge of the actions of the 178 crossbenchers - who are not aligned to any party.
Mrs May has said she wants to invoke Article 50 of the 2009 Lisbon Treaty - the formal two-year mechanism by which a state must leave the EU - by the end of March, and the government has warned the House of Lords not to frustrate the process.
Among other contributors to the debate, former Labour foreign secretary Lord Owen, who sits as an Independent Social Democrat, said: "You cannot face this issue and ignore the decision of the referendum.
"But equally well, you cannot talk about a United Kingdom without being aware of the fact that a substantial number of people did not vote for it. We have to take account of those divisions as we approach this next and most crucial stage."
And former ambassador to the EU Lord Kerr of Kinlochard, who drew up the Article 50 procedure, said it was not irrevocable and Parliament could invite the government or the country to think again.
The UK would remain a full member of the EU throughout the negotiating period and, "if having looked into the abyss we were to change our minds about withdrawal, we certainly could and no-one in Brussels could stop us", he added.
Winding up the debate, Brexit minister Lord Bridges said the bill should be passed as quickly as possible to allow negotiations with the rest of the EU to start.
A clear majority had voted to leave the EU and there could be "no attempts to remain inside and no attempts to rejoin", he told peers. He also suggested giving unilateral guarantees over the future of EU nationals living in the UK would not help British expats based in other member states.
"They could end up facing two years of uncertainty if any urgency of resolving their status was removed by the UK making a one-sided guarantee," he said.
Detailed scrutiny of the bill at committee stage is due to take place on 27 February and 1 March. If the bill is not amended, then it could theoretically be approved by the Lords at Third Reading on 7 March, becoming law shortly afterwards.
If peers do make changes to the bill, it would put them on a collision course with MPs - who overwhelmingly passed the bill unaltered and would be expected to overturn any Lords amendments.