Former Foreign Secretary Mr Johnson claimed his Brexit dream "is dying" in his scathing resignation letter.
May said she had chaired a "productive" meeting of her government, unswayed by the resignations of Foreign Secretary Boris Johnson and Brexit negotiator David Davis that rocked the government on Monday.
Davis quit late Sunday saying he could not support May's plans for close trade and regulatory ties with the bloc after the United Kingdom leaves the European Union next year.
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.
When asked whether May would contest any vote on a confidence motion in her leadership, her spokesman said: "Yes".
The Brexiteer said there had been compromise on the Leave side and there needed to be compromise on the Remain side, including getting rid of the "ridiculous notion" of having a second referendum.
So, as things stand, although a number of Conservative MPs are clearly unhappy with how May is handling Brexit, they are a vocal minority, without the numbers to actually remove the prime minister.
She looks set on facing down a rebellion in her Conservative Party, where hardline Brexit supporters are livid over her plans to negotiate "a free trade area for goods" with the EU.
Johnson said in his letter that May's plan to keep close economic ties with the bloc means Britain is heading for a "semi Brexit" that would leave Britain with the "status of a colony" of the EU.
"There was a feeling that there's a need to defend the prime minister from somebody who has made a decision for his own benefit".
She also said that the government had no intention of extending Article 50, which is a notice of intention to leave the European Union, and that there will not be a second national vote on this Brexit deal.
"I think the fact that she has lost two cabinet members has. strengthened her", he said.
"I think Dominic Raab will do a brilliant job of going in there and saying, 'This is what we want, are we going to get it and if not we have some alternatives'".
However, at a meeting with her Conservative Party lawmakers, she was cheered and applauded by many as she warned them that internal squabbling could pave the way for socialist opposition leader Jeremy Corbyn to take power instead.