Both MPs pointed to the Northern Ireland backstop, which the government signed up to in December, as a key part of how the government had ended up with what they argued was an unacceptable compromise.
May has said she will fight off any attempt to unseat her.
Brussels has not yet made clear how the EU27 will respond to the Chequers deal, which the government believes represents an "evolution" of its negotiating strategy.
The pound pared losses amid fading concerns that the resignations will immediately push May to a confidence vote.
In her resignation letter she echoed the words of Sir Michael, saying her actions "fell below the high standards" expected.
May must now quickly seek European Union support for her proposal.
The two resignations have left May badly exposed and raised questions over whether she will stand firm in her commitment to pursuing a "business-friendly" Brexit, or will be faced with more resignations and calls to quit herself.
May lacks a parliamentary majority, so she can only pass legislation if her party is united or if she obtains cross-party support.
"Brexit's contradictions can't be resolved by a Cabinet riven with splits or Parliament with parties divided on this issue".
"We will not get a clean, democratic Brexit under Theresa May and if the Conservative Party don't come to their senses, then yes, when there is a leadership contest in Ukip at the end of March next year, then I would seriously consider throwing my hat back in the ring".More news: OR cattle ranchers released from prison after presidential pardon
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"The Chequers Car Crash crosses Theresa May's own red lines, it certainly fails Labour's six tests and it is a million miles away from the kind of Brexit people thought they were getting - whether they voted Leave or Remain in 2016".
Julien Hoez, a policy analyst with Vocal Europe, an online news service, believes the prime minister is going to be safe from a leadership challenge. May replied that wouldn't be possible because of the requirements of membership, including free movement of people across borders.
The Prime Minister enduring a bruising battle today as the two Cabinet heavyweights resigned over Brexit.
His resignation this afternoon from the Foreign Office, in response to May's Soft Brexit plan agreed at Chequers on Friday, and following the resignation of Brexit secretary David Davis last night, ends a period of political prevarication we haven't seen since Boris Johnson couldn't make up his mind about whether to back Leave or Remain at the European Union referendum.
He says the Brexit "dream is dying, suffocated by needless self-doubt", and that Britain is "headed to the status of a colony", having to swallow European Union writ without "any ability to influence these laws as they are made". "That dream is dying, suffocated by needless self-doubt", he wrote.
May's response was caustic.
"I wouldn't personalise it, but what struck me when I met him he kept telling us it'll be alright, when I referenced the revenue report and how catastrophic a hard Brexit would be, he simply said that we must make sure that never happens, but gave no details".
In 1982, three foreign office ministers quit, taking responsibility for Argentina's invasion of the Falkland Islands. The UK government is in turmoil, but that has been the case for more than two years.
Even so, when May appeared in parliament on Monday afternoon, she didn't look like a woman who was facing an existential crisis.
Defence Minister Guto Bebb told BBC Radio Cymru he did not think there would be a leadership challenge soon.