In a speech to MEPs he said unless the Irish border row is resolved the deal is "zero per cent" finished as he mocked May's estimation.
May said Britain needed to explore every opportunity to break the impasse.
She told parliament that 95% of the terms of exit were agreed but the Irish border was still a "considerable sticking point".
Addressing the British parliament on Monday, May said that the United Kingdom might ask for a short extension of a planned transition period to ease its exit from the European Union, or Brexit, which is due to take place on March 29, 2019.
As May said in her speech, she rejects the EU proposal for Northern Ireland to remain in a customs union with the bloc, as that could make trade with the rest of Britain more hard, something that is opposed by the Pro-Brexit Northern Irish party DUP that has propped up her minority Conservative government.
It should have, as its longer-term aim, the agreement of a free trade deal with the European Union that delivers prosperity and sets us free to make our own laws, implement a balanced immigration policy, and reach our own trade deals around the world.
The EU says it might - and so it wants London to sign a treaty clause that could leave Northern Ireland inside the EU customs space.
The former Brexit minister - who quit over Mrs May's Chequers plan for leaving the European Union - later welcomed her "strong assurance" in the House on maintaining the integrity of the UK.
Many business leaders and investors fear internal party politics could scupper an agreement, thrusting the world's fifth largest economy into a "no-deal" Brexit they say would spook markets and clog up the arteries of trade.
Companies will suffer and criminals could benefit from the inevitable border disruption that will ensue if Britain leaves the European Union without a deal, the country's public spending watchdog said on Wednesday.
Britain and Brussels are still at loggerheads over what to do about the Irish border, which has proven to be the thorniest issue in the negotiations.
Other Labour and Conservative MPs believe that voting against the deal could allow them to table amendments which they could use to push for a softer Brexit or force the government to legislate for a fresh referendum.
Mrs May paid tribute to Sir Jeremy, saying: "I am personally grateful to him for the support he has given me as Prime Minister".
Conservative lawmaker Grant Shapps said the coming week would be unsafe for May, as pro-Brexit Tories pondered whether to try to oust her.
In an editorial in the Daily Mail, the outspoken supporter of the Conservative Party and Brexit warned rebel Tory MPs that they should stop backstabbing Mrs May.
Well Mark... she asked lawmakers on Monday for patience while the final stages of a Brexit deal are being worked out.
"It is more likely to negotiate a reversal from Brexit in 36 months than 3 months", Lamberts, who meets on a weekly basis with the EU's chief Brexit negotiator Michel Barnier, said in an interview with BI.