Britain's Foreign Minister Boris Johnson leaves 10 Downing Street in London, Wednesday, June 13, 2018.
The Government's compromise is that a minister would come to the House within 28 days of a deal being rejected to tell MPs what will happen next, but an amendment tabled by former attorney general Dominic Grieve would insist on a binding Commons motion.
The government won the vote after last-minute horse-trading, some of it in the open on the floor of the House of Commons - some behind closed doors.
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.
Just hours before the vote, the pressure on May cranked up when a pro-EU junior minister quit the government so he could back the veto proposal.
"What I agreed yesterday is that as the Bill goes back to the Lords we would have further discussions with colleagues over those concerns".
"But if the Lords amendments are allowed to stand, that negotiating position will be undermined".
"The Brexit Secretary has set out three tests that any new amendment has to meet - not undermining the negotiations, not changing the constitutional role of Parliament and Government in negotiating worldwide treaties, and respecting the referendum result".
Underlining the fear that some of her Conservatives could vote against the government, May addressed her own lawmakers at a meeting of its 1922 Committee in a last-ditch appeal for them to unite around her plans to leave the EU.
"We hope for support from all wings of the party when we bring forward Brexit policy", the spokesman said. But the government is not believed to be willing to agree to Mr Grieve's call for MPs to take control of negotiations in the last resort.
Bizarrely, this amendment actually returns the Government to its original position that the date of withdrawal from the European Union wouldn't be locked into the Bill.
"If we ended up with tariffs, in the worst case scenario we'd end up with World Trade Organisation tariffs on cars at about eight or nine per cent for both imports and exports, but we're a net importer of cars, so it would make home-produced cars far more competitive in the United Kingdom market".
In the final one, MPs voted by 321 to 40 to reject a string of Lords amendments over the post-Brexit transfer of former European Union powers to the Scottish Government and other devolved assemblies.
An alternative compromise tabled at the 11th hour by former attorney general Dominic Grieve would require ministers to get Parliament's approval for their next steps if no political agreement has been reached with the European Union by the end of November. The Lords have proposed amendments to the Bill and now it's up to the Commons to decide which, if any, changes they'll accept.
After much build-up in the press and around Westminster, Theresa May avoided a battering from the Commons over Brexit - for this week, at least.
"There's a reasonable expectation that something will emerge, but I need to work on that and more importantly work with colleagues to come up with something".
However, Devon Tory Sarah Wollaston signalled that she would back Mr Grieve's amendment. "We are trying to construct at the moment a traditional British compromise and we are trying to drag as many with us as possible both in government and elsewhere around some key elements of that compromise". How does parliament have a say in those circumstances? "And I can not bring myself to vote for it in the bastion of liberty, freedom and human rights that is our Parliament".
Another Conservative Remainer, former Cabinet minister Nicky Morgan, denied that the rebels had been "played" by the Prime Minister.
"What it does is put in place a structure if things do go as planned", she said.