That followed a tumultuous week that saw foreign secretary Boris Johnson and Brexit secretary David Davis both resign in protest over Mrs May's painfully constructed Brexit plan, claiming Mrs May was failing to deliver the clean break from the European Union the public voted for in the 2016 European Union referendum.
But by setting a deadline for May to change her approach, she said he appeared to be telling MPs that it would be "in their hands" if she didn't.
Mrs May was criticised by her own side at Prime Minister's Questions, with Brexiteer backbencher Andrea Jenkyns asking pointedly "at what point it was decided that Brexit means Remain".
With the ruling Conservative party deeply divided over Brexit, Johnson said he backed the Prime Minister but savaged her Brexit policy saying it would leave Britain in a "miserable, permanent limbo".
"We dithered and burned through our negotiating capital", Johnson told lawmakers Wednesday.
But at an earlier session of parliament, May stood firm after being challenged by one pro-Brexit lawmaker in her party to explain when she had chose to change her catchphrase from "Brexit means Brexit", to "Brexit means Remain".
Turmoil over Brexit plans has hit the pound.
In his resignation letter Mr Johnson said Mrs May's Brexit strategy killed the "dream" of breaking free from the European Union.
Supporters of Hammond's new clause, which was backed by MPs from the main opposition Labor Party, were given hope of success when the government lost a vote on another aspect of its EU Trade Bill by just a handful of votes, 305 against 301 for the government.
"We must try now because we will not get another chance to do it right", he said.
May's vulnerability in parliament, where she lost her majority in an ill-judged election a year ago, was laid bare on Monday and Tuesday when she faced rebellions from both the pro-Brexit and pro-EU wings of her party.
Boris Johnson bagged the same spot as Geoffrey Howe did to make his resignation speech in the Commons.
He said that "a fog of self-doubt has descended" over the negotiations.
In a letter to his constituents, Mr Davies said the Chequers plan on trade is "unacceptable" and revealed he was concerned that proposals to give European Union citizens preferential immigration status for work and study "will go too far".
"What should have become clear to [May] is that the Chequers proposals are completely untenable with our [party] membership in the country and the electorate", Andrew Bridgen, a Conservative pro-Brexit lawmaker, told Reuters.
A spokeswoman for May said the amendments are consistent with the original plan.
She would need to win the votes of more than half the Tories' 316 MPs to survive.
"Failure to keep our promise to the electorate will nearly certainly lead to the catastrophe of Jeremy Corbyn becoming Prime Minister and I can not sit back and allow that to happen".