Leo Varadkar said he expects the British Government to stick to the commitments it made to the European Union last December for a legally enforceable backstop to avoid a hard border between Northern Ireland and the Republic.
"Don't be under any illusion, there remains a significant amount of work to do", the spokesman told reporters.
Instead, May's team is aiming to have a deal ready for the end of the month, but that will require the political will to get over the hurdle of the Irish border question, the person said.
The fraught issue of preventing a hard border between Northern Ireland and the Republic of Ireland is still proving to be one of the main sticking points holding back negotiations.
But reports from Dublin had suggested that a deal involving an all-UK customs union in the Withdrawal Agreement, plus a separate backstop for Northern Ireland, is close to being agreed.More news: Dez Bryant ready to sign with New Orleans Saints
Speaking at the Great Catholic Conferences in Brussels, Mr Barnier stressed that Britain will remain "in all likelihood" a "neighbour, partner and ally" after March 2019.
"Backstop means backstop. And a backstop can not have a time limit".
"It's the 20-year-old fragile Good Friday Agreement peace, something that the Irish Government and indeed the British Government is a co-guarantor of, and we must work to ensure that there is no hard border, customs or otherwise, on the island of Ireland, as that is a threat to that Good Friday Agreement".
With just five months until Britain is due to leave the EU, May has yet to nail down a divorce deal, with the insurance arrangement to keep open the border between British-ruled Northern Ireland and EU member state Ireland still the outstanding issue.
Downing Street says Theresa May has told the Cabinet, on Tuesday, she is confident of reaching a withdrawal agreement with the European Union and wanted to do so as soon as possible but it must "not be done at any cost".More news: Red Star upsets Liverpool in Champions League
Kuenssberg said Mrs May and cabinet ministers were in agreement about the "horror" of missing the November deadline - a "deeply undesirable" outcome that would tilt the scales towards a "no-deal" Brexit.
"On the Northern Ireland backstop there are a number of issues that we still need to work through and these are the most hard", a spokesman for the prime minister said afterwards.
The spokesman said: "This includes ensuring that if the backstop is ever needed it is not permanent, and there is a mechanism to ensure the United Kingdom could not be held in the arrangement indefinitely".
Following the cabinet meeting, Mrs May's spokesman said: "The prime minister said she was confident of reaching a deal. The prime minister has been clear that we are making good progress on the future relationship, and 95 percent of the withdrawal agreement is now settled and negotiations are ongoing".
This was to be a "backstop" insurance clause in the Brexit treaty, to be triggered if, by the end of a status-quo transition period, no better way had been agreed to keep the Irish border operating more or less as it does now.More news: Burley doubts over Lukaku getting back into Man Utd XI
For his part, Barnier said that bargaining on Brexit is "very negative" and the deal won't bring any benefits to either side.