The government won the EEA vote comfortably after Labour abstained, although three Tory MPs, Ken Clarke, Anna Soubry and Dominic Grieve, rebelled themselves and backed the motion.
Around a dozen Tory Remainers said that May had promised them that the government would accept two parts of the amendment by Grieve, a former attorney general: a vote on the final deal and a statement from ministers to seek approval from parliament for the next steps if no deal is reached by November 30 of this year. He said he would vote against the prime minister.
She told BBC Radio 4's World At One that "at least half a dozen" junior ministers had been "very uncomfortable for some time" at the Government's direction on Brexit.
Another flashpoint could come when lawmakers vote Wednesday on an amendment seeking to keep Britain in a customs union with the EU.
"Anything that undermines the government at home will make negotiations with the European Union more hard", May told a meeting of her cabinet.
Parliament must decide whether to support an amendment approved by the House of Lords that could mean sending May back into negotiations with the European Union if lawmakers reject a Brexit deal. The strength of this commitment is yet to be seen in writing - and the Brexit department is still insisting it has not given up control of the negotiations - but the anti-Brexit rebels showed they have the numbers to force a defeat should the government renege on its pledge.
Flint said she could not support EEA membership because it would mean there would be no restriction on free movement.
Theresa May has suffered a ministerial resignation ahead of crunch Commons votes on Brexit, with Phillip Lee hitting out at the Government's "irresponsible" approach.
She has previously spoken of the threats she faced for challenging the government, and revealed that one colleague would not be voting as they wished this week for fear of reprisals.
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Today the government avoided an embarrassing defeat on a key Brexit vote by offering concessions to Remainer Tory MPs.
"We must under all circumstances respect the result of the referendum", Brexit Secretary David Davis told lawmakers as he opened the debate.
But his amendment rejecting the EEA and proposing "full access to the internal market of the EU" was a messy fudge that was too much for many Labour MPs to swallow.
Then, "MPs voted to reverse the Lords amendment removing the "exit day" from the bill by 326 votes to 301 - a majority of 25".
If May is defeated in the House of Commons it will be yet another blow to a prime minister whose authority has been challenged several times since last year's election.
May, who leads a minority government propped up by the small Northern Irish Democratic Unionist Party (DUP), conceded that "we need parliamentary support" to implement Brexit.
She said unless there was a "meaningful vote" Parliament would be left with "the grim choice between a poor deal and exit with no deal at all".
May urged Conservative lawmakers to back the government and show "that we are united as a party in our determination to deliver on the decision made by the British people".