A senior Downing Street source said she would repeat her message at a meeting of European Union leaders in Salzburg on Wednesday and Thursday that Britain was proposing "a fair arrangement that will work for the EU's economy as well as the UK's".
However, the plan faced criticism from within her own party, and triggered the resignation of Foreign Secretary Boris Johnson, who recently referred to her plans as a "suicide vest".
He said: "We have shown how that is possible, and we have published material on it".
"The pressures this causes means that we have to turn away qualified doctors, teachers, and entrepreneurs from non-EU countries who would make a positive contribution to this country".
"They made that choice".
"If the Chequers Plan is not acceptable as a basis for that, then the Government will need to find a different approach urgently". Chequers is about the future relationship.
"The alternative to that will be not having a deal", she told the BBC in an interview out Monday.
But Mr Raab rejected talk of a second vote, saying: "Even if that's what people want to do, it's hard to see how it could be done in time, and we wouldn't facilitate it".
"With goodwill and determination on both sides we can avoid a disorderly exit and reach a deal that is in the best interests of both sides".
Christine Lagarde, the IMF's managing director, told a news conference at the Treasury in London: "Those projections assume a timely deal with the European Union on a broad free trade agreement and a relatively orderly Brexit process after that".
However Mrs May has rejected the plan as unacceptable arguing that it would effectively create a border in the Irish Sea between Northern Ireland and the rest of the UK.
Mr Barnier said he was working on a plan to "de-dramatise" the controls necessary in the event of the backstop coming into play.
Writing in The Daily Telegraph, Mr Johnson said: "If the Brexit negotiations continue on this path they will end, I am afraid, in a spectacular political auto crash".
The recommendations came in a report released on Tuesday that three arch-Brexiteers who sit on the committee - Jacob Rees-Mogg, Andrea Jenkyns and Sammy Wilson - refused to endorse.
May has proposed that Britain follow European Union rules in trade in goods after Brexit, to protect manufacturing supply lines and avoid a "hard border" between Northern Ireland and Ireland.
Reiterating that Britain is committed to a "legally operative protocol on Northern Ireland", the source said May would again underline that such an agreement must respect her country's integrity, "which the Commission's proposal does not".
The party's stance on Brexit is expected to be debated at the gathering and Mr Lammy said: "A People's Vote is not only the right thing to do for jobs, public services and the future of our young people - it's the best way to get a radical Labour government".
"Unfortunately, a no-deal scenario is still quite possible".
In the interview, to be fully aired as part of the BBC's "Panorama" programme on Monday night in the United Kingdom, the premier also issues an ultimatum to critics who have questioned her strategy on Brexit.
The report notes that a no-deal Brexit would have "significant consequences for the United Kingdom and the European Union", adding: "We remain of the view that this would be chaotic and damaging for the United Kingdom economy and would leave many businesses facing huge uncertainty".