Others are calling for a public vote on the final Brexit deal before it's signed, but Ms May insisted against the need for any further public vote on Sunday.
Downing Street confirmed that Mrs May will use an informal summit of the European Council in Salzburg later this month to make the case for her blueprint direct to fellow leaders.
On a different note, in the July meeting of Labour's NEC - the last before today's one dominated by the issue of anti-Semitism - I'm told that the idea was raised of developing closer ties to the Greek and Spanish breakaway parties of the Left, Syriza and Podemos.
"I will continue to meet regularly with Michel Barnier, confident that a deal is within our grasp", he said.
Scottish independence could open up a five point lead after Brexit with the support of 47% of Scots, against 43% who say they will continue to back United Kingdom membership, according to the Deltapoll survey of 1,022 people in Scotland.
"We have made significant progress, we are making significant progress every week. and a deal is within our sights", he said.
Raab told lawmakers in the House of Commons that the two sides had "injected some additional pace and intensity into the negotiations as we reach the final phases".
Conservative MP and former government minister Nick Boles, who during the referendum backed remaining in the European Union and now wants to stay in the single market on an interim basis while negotiating a "Better Brexit" free trade deal, said he didn't think May had enough support for her proposals.
The Eurosceptic ex-cabinet minister said the proposals put forward by Mrs May would be "worse than staying in" the European Union. "You can inflate the hard border with Ireland by blowing on this whistle."A no-deal scenario would bring some countervailing opportunities", he continued, "including a swifter end to our financial contributions to the EU."This, arguably, is one the airline industry might consider actually taking up: "Hello, this is your captain speaking".
With Parliament due to return Tuesday from its summer break, Johnson and his fellow Brexit enthusiasts aren't the only obstacle May faces as she tries to get her Brexit deal past her Conservative Party, Britain's Parliament and the EU.
Remain supporter and former Education Secretary Justine Greening said the plan unveiled at Chequers was "now dead", and argued there was "no point having a government spending two vital months working on that" when it should be drafting a new pathway to Brexit.
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Johnson used his newspaper column yesterday to accuse some members of the government of deliberately using the Irish border situation to "stop a proper Brexit", a claim rejected by Whitehall sources.
One of the committee, former Conservative minister John Whittingdale, said it had become clear in the meeting that the European Union "just can't accept" the Chequers plan, because it thinks it goes against the principles of the single market.
Campaigners for a second referendum said the findings showed the need for Britain to think again.