After bowing to pro-Brexit lawmakers in her party on Monday, the prime minister may have opened the door to their growing calls for her to ditch the Chequers plan.
But he insisted: "It is not too late to save Brexit".
Referring to further betrayals and weak negotiating, Johnson cited a "fog of self-doubt", "stealthy retreat", and dithering within Westminster.
A string of ministerial resignations followed, including that of former Foreign Secretary Boris Johnson and Brexit Secretary David Davis, the former still being touted by a replacement for May should a contest arise.
Mrs May later defended the Government's acceptance of Brexiteer amendments to key legislation before insisting its "facilitated customs agreement" plan for the European Union has not been abandoned and is being discussed with the EU.
One eurosceptic source said: "We drew up that amendment so it would be unacceptable, so that they would have to fight and lose". Labour also says the June 2016 referendum vote to leave the European Union must be respected but has attacked the PM over the splits in her party.
May's words, to be delivered at the Farnborough Airshow south west of London, come at a crunch time for the prime minister as pro-Brexit lawmakers in her party threaten revolt over an European Union exit strategy they say leaves Britain subject to Brussels' rule.
The third reading of the government's Trade Bill was passed comfortably by 317 votes to 286, with peers now set to scrutinise the legislation.
"There is time, and if the prime minister can fix that vision once again. then I believe she can deliver a great Brexit for Britain", he said.
During a tense session in Westminster, the Prime Minister thwarted the Tory rebellion by 307 votes to 301, helped by four Labour Brexiteers who cast their ballots against their own party.
May vows to stick to her plan to negotiate the closest possible commercial links - "a common rule book" for goods - with the bloc, saying this is the only way to balance political and economic priorities for Brexit, the most momentous shift in British foreign and trade policy for decades.
He said: "This has not been an easy decision and I have agonised over it, but I know in my heart of hearts it is the right decision".
While Johnson was delivering his speech May was along the corridor in the Houses of Parliament facing a grilling from a liaison committee, made up of every chair of every House of Commons select committee. "We have to have a compromise position that enables the country to get an agreement with the European Union", trade minister Liam Fox told BBC radio.
Thus, the fact that twelve of Mrs May's colleagues were willing to vote against her, even with the possibility of bringing down the government, shows the frail grip she has on her party.
Conservative International Trade Minister Liam Fox argued that the legislation will provide "stability and continuity" to companies until the United Kingdom can reach its own trade deals at the end of the 21-month transition period following Brexit, which will be enacted on March 29, 2019.