Taoiseach Leo Varadkar downplayed the prospects of the European Union countenancing amendments to a text that has taken two years to develop. "I think in a no-deal scenario it would be very hard to avoid a hard border".
"If there is a hard border between mainland Britain and Northern Ireland, and Northern Ireland remains part of the Customs Union in any final status, you've effectively broken up the United Kingdom", he said.
Acknowledging Mrs May has "quite a battle" to get the draft document through the House of Commons, Mr Varadkar said: "She is someone who has shown enormous resilience in the past".
"We can avoid a hard border by signing up for the agreement that has been negotiated", Varadkar told reporters.
Irish Prime Minister Leo Varadkar said he did not consider renegotiating the Brexit agreement possible, regardless of who holds the position of Brexit Secretary.
"I think people should take some time to read the full implications of what this will mean".
The so-called Northern Ireland backstop, which aims to keep the border between the British province and EU member Ireland open, would all but leave Northern Ireland inside the EU's single market if an eventual British/EU trade deal can not maintain the now frictionless frontier.
"But that would have to be requested by the UK Government and they have been very clear. that they won't be seeking a delay", he added.
"We have to be prudent, we have to prepare for the worst case scenario is even though I'm much more confident now that the worst case scenario won't arise", he said.
Outside Dublin's government buildings, Mr Eastwood said that hard days lay ahead for Prime Minister Theresa May, but the group's focus was on Northern Ireland.
The Brexit deal is complex and unwieldy.
After the meeting, Sinn Fein leader for Northern Ireland Michelle O'Neill said: "We have had a very positive meeting, where we were able to seek some assurances over what has been achieved in the agreement so far".
Mr Varadkar said it does not make sense to say that "goodwill" alone can keep the border open.
Labour former minister Kate Hoey later added: "Outside this House when people read these hundreds of pages of eurospeak, they will realise that in any way we are being sold out, we've been sold out by our negotiators who have allowed the European Union to take the lead".