The main point of contention between those who want to keep the closest possible ties with the European Union and those who aim for a clean break is a demand to give parliament a "meaningful vote" on any agreement May negotiates with Brussels.
Just three hours later, ministers caved in.
A majority of MPs defeated attempts to turn the prime minister's Brexit policy on its head on Wednesday.
As Tory rebels threatened to defy the whip and back the Lords' amendment, .
Some lawmakers tried to shout him down and accused the government of wanting too much power. Many of its pro-EU lawmakers went against their leader, Jeremy Corbyn, by supporting the vote and not his amendment which argued for a new single market deal with the EU.
The vote on Tuesday is the first of two days of debate that will test May's authority and her plans for leaving the EU.More news: Norwegian lawmakers nominate Trump for Nobel Peace Prize
He said that remaining in the EEA, which includes membership of the single market, was not a ideal solution.
An agreement that defused a potential rebellion over handing parliament more control over Britain's exit from the European Union looked in danger of unraveling on Wednesday, when the two camps argued over the shape of a possible compromise on a "meaningful vote".
"The prime minister said that the votes were important in terms of the message they send to Brussels", May's spokesman said she told her cabinet team of ministers.
But the rebels were split, with 74 voting in favour of the Lords amendment, which called for the Government to pursue the so-called "Norway Model" membership, and 15 against it. The strength of this commitment is yet to be seen in writing - and the Brexit department is still insisting it has not given up control of the negotiations - but the anti-Brexit rebels showed they have the numbers to force a defeat should the government renege on its pledge.
But in unusual scenes, ministers were forced to offer a last-minute compromise to pro-European MPs, negotiated in part in huddles in the chamber as the debate raged.
May has promised to give the British parliament a vote on the final deal, but the question is what happens if lawmakers decide to reject it. The government earlier had said it would not support that amendment.More news: British PM fends off Brexit parliamentary defeat
But that vote required last-minute concessions to pro-European Tories, and they warned Wednesday they could yet seek to defeat the government if May fails to fulfil her promises.
Theresa May has suffered a ministerial resignation ahead of crunch Commons votes on Brexit, with Phillip Lee hitting out at the Government's "irresponsible" approach.
Attempts to keep the United Kingdom in the European Economic Area after Brexit have been defeated in the House of Commons, amid a major Labour revolt over the issue.
Talks with Brussels have stalled over the fraught issue of the Irish border, but both sides are hoping to agree a deal by October in time for the Brexit date of March 29, 2019.
There was little doubt the government would win on the customs union and single market, which some pro-EU lawmakers say is the only way for Britain to retain economically advantageous close ties with the bloc, with the opposition Labour Party also divided over future relations.
It has been clear for a while that the now ex-minister, one of the rising generation in the Tory party, has been frustrated for some time.More news: Added Sugar Consumption In Toddlers Is On The Rise In The US
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