Meanwhile Irish Taoiseach Leo Varadkar has also sought to turn up the heat by claiming Britain faced economic disaster if the House of Commons fails to ratify the deal, with Mrs May forced into a u-turn weeks later.
The 565-page draft agreement was unveiled on Wednesday, with negotiations beginning this weekend in advance of Friday’s summit in Brussels to discuss the matter.
However, since the publication of the document, various members of the EU 27 have voiced concerns about different aspects of the proposals.
Some fear Britain would have an economic advantage after Brexit if permitted to diverge from European laws and regulations while retaining access to the single market, while others want greater powers for the European Court of Justic and improved fishing rights in UK waters.
One Brussels negotiator told The Times that France, Spain, Belgium, Denmark and Portugal were among the European countries unhappy over the issue of UK fishing rights.
Diplomatic notes suggest France wants a “guarantee that there should be a fisheries agreement” allowing French and other European fleets access to British waters.
Meanwhile, Italy, the Netherlands, Denmark and Germany are concerned the EU’s offer of a customs union to avoid a hard border in Ireland could offer Britain an economic advantage.
They also want the ECJ to be empowered to prevent Britain undercutting EU social and environment standards.
Another diplomat said: “We are concerned that the UK is getting what it wants, which undermines the level playing field of the single market.”
However, a European ambassador warned: “The withdrawal agreement is a good one for the EU and the danger is that by demanding too much in the way of conditions on Britain it will be wrecked.”
Meanwhile Ireland and Germany are among those insisting “customs backstop cannot be unilaterally withdrawn”, the key reason for Brexit secretary Dominic Raab’s resignation on Thursday.
Mr Varadkar also had some words of warning for Mrs May, saying: “A no-deal Brexit would be extremely chaotic. After a few weeks the UK might sign a deal.”
Leaders have also sought to emphasise there will be little or no room for manoeuvre when Mrs May travels to Brussels.
Austrian chancellor Sebastian Kurz, who currently holds the EU’s rotating presidency, said: “It is a good deal for both sides, nobody has been cheated.
“This deal prevents a hard Brexit.
“Therefore it helps us in Europe, but even more so it helps Great Britain because a hard Brexit would hit Great Britain significantly more severely.”
Dutch Prime Minister Mark Rutte said: “It is highly unlikely that we will make important changes to these proposals,” he said.
Bruno Le Maire, the French finance minister, said: “The choice now faced by British political leaders who have advocated Brexit is to renounce their absurd political promises or face economic disaster, with the British people the main victims.”
A senior EU diplomat added: “Merkel, Macron and all of them will line up to say this is the agreement.
“It is on the table. It is the only deal. There is nothing else.”