The Democratic Unionist Party (DUP) is the other big issue for the prime minister, who relies on the Northern Irish party's votes to give her a notional majority in parliament.
A particular source of contention is what the "backstop", the fallback option for border arrangements in the event the two sides can not reach an agreement by the end of the transition period, will look like.
Speaking to Northern Ireland journalists at her Downing Street office, May said on Thursday that talks on the Irish backstop were likely to continue until November.
Her intervention came as Mrs May met key members of her cabinet in Downing Street to brief them on the progress in the Brexit negotiations.
The EU's chief negotiator Michel Barnier on Wednesday said Britain must accept possible checks on goods moving between its mainland and its province of Northern Ireland, saying Brexit would trigger the need for customs, value-added tax and compliance checks with EU standards.
Writing in the Telegraph, Sammy Wilson MP, the DUP's Brexit spokesman, said Mrs May was pursuing "the road to parliamentary defeat" because his party would vote against any deal that included the proposed backstop. Michael Russell will be there representing the Scottish Government and is expected to once again sound the alarm about the damage to Scotland's economy a hard or no-deal Brexit would do.
Mr Coveney said: "It is a deal breaker".
Earlier, asked several times if she backed Mrs May's approach, set out in a White Paper in July, Ms McVey told the BBC: "I am completely supportive of the prime minister as she well knows, what I won't do even for you right now is speculate".
It came as Mrs May's "inner cabinet" was briefed last night on plans for a no-deal Brexit amid reports that progress ahead of a crucial European Union summit next week had been slower than hoped.
"An agreement is within reach", he said.
The UK is expected to come up with new proposals as an alternative to the "backstop" put forward by the European Union - which the government has rejected, saying it would threaten the integrity of the UK.
On Wednesday it was revealed that the DUP was prepared to vote against the Budget on 29 October - which could threaten the future of the government - if there are any new barriers between Northern Ireland and the rest of the United Kingdom as a result of Brexit.
While some Tory MPs have said they believe the DUP is "bluffing" about withholding its support, Mr Wilson yesterday warned: "Do not take our votes for granted".
Staying in a customs union would stop Britain from negotiating new trade deals.
"For my perspective, to be blamed for Brexit when I neither supported the referendum or supported Brexit is a little bit tribal, unreasonable, I would say", he added. Checks of animals and animal-derived products would still have to take place between Northern Ireland and the rest of the United Kingdom and cover all of that trade.