Mrs May has repeatedly ruled out being in a customs union with Brussels after Brexit on the grounds it would leave Britain too closely tied to the EU.
The party's European Research Group says it will reject any last attempts at compromise by Number 10 as they hope to force May to change course over Brexit or risk a no-confidence vote before the summer break by demonstrating the depth of their support.
Fresh from her pyrrhic victory yesterday, the Prime Minister is to go head-to-head with Remainers over another Brexit bill - this time on trade - and her decision to start MPs' summer holiday on Thursday this week, instead of Tuesday next week. Earlier, a ministerial aide also resigned in protest at what he called a "watered-down Brexit", underlining the pressure on Mrs May from both sides of her party.
"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".
"This could lead to a damaging and disorderly Brexit", she wrote. She added: "I have always said I'm in this for the long term".
The amendment, tabled by pro-EU Conservative MPs Stephen Hammond and Nicky Morgan, was defeated by 307 votes to 301.
French fans give hero welcome to 'Les Bleus' World Cup champions
The team's Air France plane was given a traditional water shower by firefighters as it taxied around the tarmac. The French squad celebrating from the bus with the crowd.
She told MPs: "I would not have gone through all the work that I did to ensure that we reached that agreement only to see it changed in some way through these bills".
May said the plan outlined in the white paper honors the wishes of British voters - who in June 2016 backed Brexit with 52 percent of the vote - while protecting industry and security.
May claims that the trade bill will enable Britain to maintain the 40-odd trade agreements that the European Union has with countries around the world. He added: "I can not tell the people of WOxon [West Oxfordshire] that I support the proposals in their current form".
The bill is also due to have its third reading on Monday, and it could be in jeopardy if the angry Tory Brexiters join with Labour, the SNP and the Lib Dems, who are expected to vote against it.
"And if everyone has to put a second option, everyone's going to put the Chequers deal".
Parliament will debate aspects of the Brexit plan later Monday.