He renewed his public campaign for a second referendum on Friday with a new speech warning Mrs May's deal was in "crisis" and a vote was the only answer.
"No, a second referendum would be divisive", British education minister Damian Hinds said.
During Friday's meeting with the four leaders, May said the U.K. -EU deal had no chance of surviving as written because her own Conservative Party and Northern Ireland's Democratic Unionist Party - which props up her minority government - will never support the so-called Irish backstop in its current form.
On Thursday about 10 Labour MPs met David Lidington - who is Mrs May's de facto second-in-command - to argue for another public vote.
Former Prime Minister Tony Blair.
But Labour leader Jeremy Corbyn said her deal was now "dead in the water" and the prime minister had "utterly failed in her attempts to deliver any meaningful changes".
Lidington replied that he always listened to MPs' views but pointed to recent remarks in parliament where he said a second referendum may not be decisive and could damage confidence in democracy.
Noting the strikingly angry tone, the BBC reports Mrs May said on Saturday, "For Tony Blair to go to Brussels and seek to undermine our negotiations by advocating for a second referendum is an insult to the office he once held and the people he once served".
A crucial parliamentary vote on Mrs May's deal has been deferred until the New Year amid speculation that it would the heavily defeated in the Commons.
Mr Varadkar said he could not speak for the EU27 but he expected if the alternative was Britain crashing out of the European Union in March, then the European Union would grant an extension.
Separately, Foreign Minister Jeremy Hunt suggested Britain could thrive if it left the European Union with no deal, and admitted he would like to "have a crack" at May's job.
Weeks ago only a marginal issue, now dozens of Labour MPs are backing another vote, as well as the SNP, Liberal Democrats, and smaller parties.
The problem for pro-Brexit members of May's Tory party is that there is no way for Britain to leave the backstop without the EU's agreement.
He urged politicians to back the PM's plan, describing it as "balanced" and the "best of both worlds".
"We've faced much bigger challenges in our history", he said.
He also said reports that relations with the United Kingdom were being handled by Tánaiste and Minister for Foreign Affairs Simon Coveney were not true and lines of communication between himself and Mrs May personally and his office and Downing Street are kept open.
Parliament was supposed to vote on the deal this week, but May postponed it after it became clear that lawmakers would decisively reject it. Anger at the postponement triggered a no-confidence vote in May's own Conservative Party.