As Britain is entering the final stages of Brexit negotiations, May said, now is the time for "cool, calm heads."
She reminded the MPs that both the UK and the EU share the responsibility to preserve the Belfast 'Good Friday' Agreement, protecting peace and stability in Northern Ireland.
The unique circumstances in Northern Ireland and the timeframe of the Brexit implementation period create the need for a backstop, May argued. The backstop policy would serve as an "insurance policy for the people of Ireland and Northern Ireland."
And even though, the European Union have agreed to explore a UK-wide customs solution to the backstop, two problems remain, Theresa May told the MPs, at which point the parliamentarians burst into laughter.
"First, the EU says there is no time to work out the detail of this UK-wide solution in the next few weeks, so even with the progress we have made, the EU still requires a backstop to the backstop — effectively an insurance policy for the insurance policy. They want this to be a Northern Ireland only solution that they had previously proposed," Theresa May said.
Second, explained the PM, she should be able to promise the British people that the backstop is only a temporary solution, which won't become "a permanent limbo."
"I am clear we are not going to be trapped permanently in a single customs territory, unable to do meaningful trade deals. So it must be the case that the backstop should not need to come into force and second — if it does, it must be temporary. And third: while I don't believe it will be the case, if the EU would not cooperate on our future relationship we must be able to ensure that we won't be kept in this backstop arrangement indefinitely."
The PM stressed that the government must not let the backstop issue disagreement "derails the prospects of a good deal," leaving the country with "a no deal outcome that no-one wants."
The backstop proposed by the European Union would see Northern Ireland staying in the EU customs union, large parts of the single market and the EU VAT system.
According to EU's chief negotiator, Michel Barnier, the backstop would only apply to Northern Ireland.
The leader of the Democratic Unionist Party of the Northern Ireland stressed on Monday, that there cannot be any "economic barriers between Britain and N. Ireland."
Barnier's proposal is not best of both worlds, Arlene Foster added, speaking in Dublin.
The DUP leader said that nobody wants to see physical infrastructure on Irish border and expressed hope a sensible Brexit deal can be achieved.
Answering a parliamentarian's question, May dismissed the idea of a second Brexit referendum.
"The people have already voted on Brexit," the PM told the Parliament.
French President Emmanuel Macron said he will discuss Brexit with Theresa May later on Monday. He reportedly said he was prepared for all scenarios.
Over the weekend, the UK and EU negotiators have made "progress in a number of key areas."
In the last few days UK and EU negotiators have made real progress in a number of key areas. However there remain a number of unresolved issues relating to the backstop.— Exiting the EU Dept (@DExEUgov) October 14, 2018
The UK is still committed to making progress at the October European Council.
The issue of a backstop still very much stands in the way of a Brexit deal, as the deadline for Britain's exit from the European bloc, as well as the need for an agreed exit plan fast approach.