The move has fuelled accusations on social media from Labour MPs and journalists, amongst others, that the May government was "afraid of their own MPs" and 'seeking to function'.
May now faces rebellion from the pro-EU flank of her Conservative party, who are outraged by her caving in to these harder Brexiteer demands.
But Labour MP Stephen Kinnock accused the PM of "capitulating" and said the Chequers deal was now "dead in the water".
Plus Andrew Griffiths, a key ally and former chief of staff for Theresa May resigned this weekend over inappropriate sexual texts to constituents, making 10 government resignations in just 8 days.
It gives the government the power to build new trade relationships around the world after the United Kingdom leaves the EU, and MPs who support staying in the EU's customs union are seeking to change its wording.
On Monday night Brexiteers narrowly defeated Tory rebels by just three votes on two amendments.
"[But] they are wondering if the prime minister - or anyone who could or might take over from her - would even have the political strength to get a deal agreed here in Brussels, then passed by parliament back home".
If Mrs May holds on as leader and manages to rally her troops behind the Brexit plan agreed by the Cabinet at Chequers, she still faces the tough challenge of winning the European Union over to her proposals.
Brexiteers had set up a WhatsApp group to co-ordinate voting tactics, organised by ex-Brexit minister Steve Baker, who quit over the Chequers plan.
Former global development secretary Priti Patel, who is proposing one of four amendments to the Taxation (Cross-border Trade) Bill, told BBC Radio 4's Westminster Hour the white paper had "many flaws around our independence and our ability to make free trade agreements".
Tory MP and Remainer Heidi Allen said she wished the prime minister had "faced down the amendments".
"The Tory government is riding roughshod over the Scottish Parliament's voice on Brexit".
The ex-foreign secretary used a Daily Telegraph column to ominously say "I will resist - for now - the temptation to bang on about Brexit".
Meanwhile the Electoral Commission announced it was fining Vote Leave, the official pro-Brexit campaign in the 2016 referendum, for breaching spending limits and refusing to cooperate with its investigation.
She insisted it would allow Britain to control migration, end the jurisdiction of European Union courts and forge its own trade policy - despite US President Donald Trump saying it could "kill" a US-UK trade deal. I think it was a genuine clever attempt at a compromise that could work.
Mrs May faced a potential revolt on the Taxation (Cross-border Trade) Bill, often referred to as the Customs Bill.
"Parliament is now stalemated on a way forward on Brexit, if it's the prime minister's deal it will be voted down, if it's a proposal for no deal that will be voted down, all parliament can do is block a route forward".
Un résultat qui n'a pas du tout entamé le fairplay ni la sympathie de la présidente de la Croatie , Kolinda Grabar-Kitarovic. Les Croates auront plutôt tendance à serrer la main des inconnus et à faire des accolades à leurs amis.
And so, yes, I think we have elevated this Russian Federation thing to a degree that we are simply deranged by it. And apparently, Trump was digesting it too, and reflecting on the criticism that came pouring in from all sides.
Earlier Monday, Trump blamed Mueller's investigation into Russia's campaign meddling for hurting relations between the countries. After the glider appeared, Trump was seen cutting across the grass, quickly heading to the entrance of the resort.
Japanese consumers have historically coveted European products, and a drop in prices is likely to boost spending. Juncker said the deal sent a message that "trade is about more than tariffs and barriers, it is about values".
She now argues a referendum should "give the public a first and second preference vote, allowing a consensus finally to be found". A Labour source said: "It is staggering that the Tories are in such a state they are considering just packing up and going home".
Croatia greeted by 500,000 fans in return home after World Cup
The Didier Deschamps managed side secured an exhilarating 4-2 victory over Croatia, prompting an outpouring of joy across France . While, in Russian Federation , the 40-year-old president was spotted jumping for joy and pumping his first with each goal.
The Reason Kylie Jenner Removed Her Lip Fillers
Other people defended Kylie , noting that she is still a successful businesswoman, and that people should respect her as such. She continued, "Nobody works harder than my sisters and my mom".
Liverpool FC sign Xherdan Shaqiri on five year contract
Liverpool have signed Swiss worldwide Xherdan Shaqiri from Stoke City , the English Premier League giants announced Friday. Liverpool on the other hand, needed a profile to boost their attack. "It's good that they can come".