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.
Britain says Brexit won't mean physical customs checks.
The stumbling block seemed to be May calculating that an European Union demand for a special "backstop" clause for Northern Ireland could not win support from her own party and allies in parliament - at least not just for the moment.
Mrs May will tell the Commons that "taking all of this together, 95% of the withdrawal agreement and its protocols are now settled".
The pound rose above $1.29 on Thursday after a show of support for British Prime Minister Theresa May from her Conservative Party dampened fears of an immediate leadership challenge over her Brexit strategy.
This would mean that initially the backstop would keep the United Kingdom inside the customs union for a period of six months or one year.
He said the "insurance mechanism" must be agreed to first before the withdrawal deal is confirmed and it must remain in place "unless and until something better is agreed".
The UK should be able to make a "sovereign choice" in December 2020 between extending the transition period for a short period or keeping the whole of the UK in a temporary, time-limited customs arrangement with the European Union, she said.
Her shift aimed to break an impasse in negotiations between London and Brussels over how to keep the Irish border open after Brexit, by giving the two sides more time to agree their future relationship.
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But she will add: "As I set out last week, the original backstop proposal from the European Union was one we could not accept, as it would mean creating a customs border down the Irish Sea and breaking up the integrity of the UK".
Sir Keir Starmer said the current deadlock is a "mess of the Prime Minister's own making" and warned she is unlikely to survive if she can not secure support for her plans.
He told them that, though they had been promised a "meaningful" vote on the eventual Brexit deal made with Brussels, the vote would be a take-it-or-leave-it option.
The former Brexit secretary insisted "we should not allow ourselves to be bullied by the EU" and warned the bloc has plenty to lose from a no-deal Brexit.
With a matter of months to go until Britain leaves the EU, Mrs May is facing mounting pressure from Leavers and Remainers both inside and outside her party.
But the withdrawal agreement, or the terms of Britain's divorce, can not be signed off until the two sides agree on the Northern Irish backstop.
The Sunday Times newspaper said 46 had now been sent and the BBC's political editor said on Monday that the 48 number had not yet been reached. Under party rules May needs to win the support of just over half - 158 - to win a vote of no confidence, but many believe that she may not be able to continue as prime minister if more than 100 MPs were to vote against her.
A senior Labour figure who backs the move told The Observer: 'There are some supporters of a second referendum who think the main push should come later, amid the chaos that would ensue from May's deal failing to get through parliament or a no-deal.
It is not clear if Mr Raab's comments signal a clear split between Mrs May and her Brexit secretary on the issue.