While some were pushing back at Tusk, others believed his remarks - and the impasse they represent - shine a poor light on May, who can't seem to close this deal.
Sammy Wilson of Northern Ireland's Democratic Unionist Party tweeted that Tusk was a "devilish euro maniac. doing his best to keep the United Kingdom bound by the chains of European Union bureaucracy and control". "Sounds more like heaven to me".
And DUP Brexit spokesman Sammy Wilson tweeted: "This devilish euro maniac is doing his best to keep the United Kingdom bound by the chains of European Union bureaucracy and control".
Some Brexiteers have predicted that the EU's seemingly stubborn stance is only a negotiating tactic and Brussels will eventually succumb to United Kingdom pressure and offer a better deal with an altered or removed backstop.
She is due to meet Mr Tusk as well as European Commission president Jean-Claude Juncker and chief Brexit negotiator Michel Barnier on a visit to Brussels on Thursday.
Varadkar said the Brexit deal, which was rejected by the United Kingdom parliament, was "the best possible".
"A sense of responsibility also tells us to prepare for a possible fiasco", Tusk said.
May's opponents, meanwhile, urged the government to delay Brexit, saying Britain is unprepared to leave on March 29.
"Parliament voted by a significant margin to set out what it wishes to achieve, which is changes to the backstop", the Number 10 spokesman told reporters. In an incendiary claim that threatens to blow up Theresa May's hopes of a renegotiation of the Irish border, the EU Council President used a press conference with the Irish premier to say he "wondered" what the place looks like.
"In the event of a crash. she must as a democrat return to the Good Friday Agreement and she must begin preparation for a referendum on Irish unity", Sinn Fein leader Mary Lou McDonald said, referring to the peace accord signed in 1998 that ended three decades of sectarian violence in Northern Ireland. The E.U.is first and foremost a peace project. "It's a European issue and that's why we cannot accept the idea that the withdrawal agreement could be reopened", Juncker said, adding that the backstop was part of the November agreement.
But - and it's a big but - they have all been open to the prime minister coming to Brussels with a solution to break the deadlock.
Mr Tusk could be heard replying: "Yes, I know", before the Irish PM responded: "But I know you're right". "We will not gamble with peace or put a sell-by date on reconciliation", Tusk said.