Under Conservative rules, a confidence vote in the leader is triggered if 15 percent of Conservative lawmakers-currently 48-write a letter to the party's 1922 Committee of backbenchers, which oversees leadership votes.
May has strongly defended her draft deal amid calls for no-confidence and a flurry of resignations.
Mr Raab said: 'If we can not close this deal on reasonable terms we need to be very honest with the country that we will not be bribed and blackmailed or bullied and we will walk away.
May, who has defiantly vowed to stay on as prime minister, spoke on a radio phone-in show to defend her deal, and was asked by a caller on LBC radio to "respectfully stand down".
May is determined to fight on, warning abandoning her Brexit plan, with Britain's withdrawal just over four months away on March 29, would plunge the country into "deep and grave uncertainty".
Mrs May's de facto deputy, David Lidington, praised her resilience in carrying out the "absolutely back-breaking job" of delivering a Brexit deal and urged her critics to rally behind her in the "national interest".
A 2016 referendum to pull Britain out of the European Union won narrowly.
Another pro-Brexit minister, global trade secretary Liam Fox, also spoke out in her favour, urging MPs to support the premier's draft Brexit agreement, saying a "deal was better than no deal". Meanwhile, the European Union has already indicated that it was not willing to re-negotiate another deal and is keen to press ahead with getting the remaining 27 member-states to sign off on the current plan.
May now faced the tough challenge of pushing her proposed deal through the House of Commons, the lower chamber of United Kingdom lawmaking.
As furious Conservative rebels try to gather the numbers to trigger a no-confidence vote, May insisted she hadn't considered quitting.
In her first interview in her new job, Ms Rudd called on any colleagues planning to submit letters of no-confidence in Mrs May to "think again". "Politics is a tough business and I've been in it for a long time".
"I think it is probably imminent".
Coveney said talks in the coming days on the declaration provided British ministers with the opportunity to get the reassurances they need on future EU-British trade.
According to the BBC's political editor Laura Kuenssberg, the group of ministers want a change in the text to include the possibilities of new technology or a free trade deal as alternative solutions to the Irish border issue.
The Sunday Times also reported Britain's army had been ordered to step up contingency plans to help police maintain public order in case of food and medicine shortages after a "no deal" Brexit, citing an unnamed "well-placed army source".
However, if May is unable to get a deal through then a no-deal Brexit becomes the default position.