The Cabinet ministers were speaking as MPs prepared for the third day of debate in the House of Commons ahead of next Tuesday's crunch vote, with Home Secretary Sajid Javid opening proceedings which are expected to be dominated by the issue of migration.
But in a possible sign that the tide is beginning to turn in favour of the Prime Minister's exit plan, four Brexiteer backbenchers have announced they will back it despite speculation they could vote against it.
Failing to do so "would be a catastrophic and unforgivable breach of trust in our democracy", she wrote in a commentary published by the Sunday Express.
It was the second setback in 24 hours for the prime minister, after MPs also voted to deny the government certain taxation powers in a no-deal scenario - an attempt to scupper that prospect.
Were such a plan to succeed, the government would lose control of parliamentary business, threatening its ability to govern, putting Brexit legislation at risk.
May looks little closer to securing the support she needs, but said lawmakers must not let down the people who voted for Brexit.
Sir Vince said this could happen by cancelling Article 50 - which he noted would be "resented by lots of people" - or via a second referendum.
Liberal Democrat Brexit spokesman Tom Brake said: "Chris Grayling has lost the plot".
She continued: "When you turned out to vote in the referendum, you did so because you wanted your voice to be heard".
'Some of you put your trust in the political process for the first time in decades.
Grayling, who campaigned to Leave the European Union, said the millions who voted for Brexit would feel "cheated" if the United Kingdom did not quit the bloc.
He has since become a vocal critic of the Government's Brexit plans, urging ministers to take a tougher stance in divorce talks.
"So my message to Parliament this weekend is simple: It is time to forget the games and do what is right for our country".
Major warns that it would be "morally reprehensible" to slip into a no-deal Brexit, saying: "The cost.to our national wellbeing would be heavy and long-lasting".
Dominic Grieve, the former attorney general, suggested the March 29 exit date should be removed from domestic legislation if the prime minister's Brexit deal is defeated, before the United Kingdom goes to the European Union to ask for an extension to Article 50.
More than 100 MEPs from 26 European Union member states signed a letter calling on the United Kingdom to "reconsider" the Brexit decision, saying the UK's departure will "weaken all of us".
Part of Mrs May's Brexit deal includes plans for an "ambitious, wide-ranging and balanced" trade agreement, but the text is not legally binding.
The EU is waiting to see the outcome of Tuesday's vote - and the margin of the expected defeat - before considering its response, officials said, with some predicting that May will have to delay Brexit.