And various Tory backbenchers, including leading Brexiteer Jacob Rees-Mogg, said they had submitted letters of no confidence in Mrs May to the chairman of the Conservatives' backbench 1922 Committee.
Theresa May has dismissed speculation she could be ousted as prime minister over her Brexit agreement, saying: "I am going to see this through".
There would be "ambitious customs arrangements" that "build on" the arrangements in the withdrawal agreement.
Much of the opposition to the draft deal has focused on the Irish backstop, yet May insisted before MPs earlier that this was an insurance policy which neither side wanted to have to use. Avoiding a hard border in Northern Ireland was one of the main sticking points. They believe that bringing them back would put the peace process at risk. "Only if, and the end of transition extended or not, we are still not there with the future agreement would the backstop decision agreed today kick in".
Northern Ireland would have special status under the proposals, meaning that some checks may be required between Northern Ireland and the rest of the country.
Starmer said he thought there was zero prospect of Labour being able to work with May to achieve a softer Brexit, because the prime minister would never sign up to the opposition's demand to remain in a permanent customs union with the EU.
More ominously, the Northern Irish party propping up May's government threatened to break their alliance over leaks about a special arrangement for the British province.
The Prime Minister emerged from a marathon five-hour meeting of senior ministers yesterday evening saying there had been "collective decision" on the draft withdrawal terms, hinting at deep divisions within her government.
Tory MP Mark Francois said, with Labour, the SNP, the Lib Dems and the DUP planning to vote against it - alongside, he said, more than 80 Tory MPs, it was "mathematically impossible to get this deal through the House of Commons" and it was "dead on arrival".
Among other Cabinet ministers to resign is Work and Pensions Secretary Esther McVey, who told May the agreement does not "honor the result of the referendum, indeed it does not meet the tests you set from the outset of your premiership".
They will then have to decide whether to accept it or risk the United Kingdom leaving the European Union on March 29 without an agreement, something business groups fear could cause economic chaos.
Their departure, and the resignations of two junior ministers, shakes May's divided government.
"If nothing extraordinary happens, we will hold a European Council meeting in order to finalise and formalise the Brexit agreement", European Council President Donald Tusk said after meeting EU chief Brexit negotiator Michel Barnier. "It will take place on Sunday the 25 of November".
But MPs lined up to tell Mrs May that it could not pass, Brexit hardliners who see the deal as conceding too much to Brussels, to European Union supporters, several of whom called during Thursday's session for a second referendum.
Northern Ireland minister Shailesh Vara was the first to resign over Mrs May's agreement on Thursday morning, saying, it "leaves the United Kingdom in a halfway house with no time limit on when we will finally be a sovereign nation".
Speaking before a hostile parliament after several ministers quit on Thursday, the leader of Britain's Conservative party told legislators "the choice is clear". But, rather than force a run-off vote against Theresa May, she withdrew from the contest. She may seek to renegotiate with the European Union but most expect her time in No 10 to end.
Numerous MPs were contacted for comment but, although it is widely expected the vast majority will back the prime minister, most were unwilling to fully back Mrs May at this stage.