She told Today: "There have been periods in our history when we have had national unity governments or a coalition for a very specific issue".
May's government and her party, which has grappled with schism over Europe for 30 years, was in open conflict between those pushing for a customs union with the EU and eurosceptics who are demanding a cleaner break with the bloc. The second goes further, calling for Britain to stay in the EU's borderless single market for both goods and services.
But pro-EU commentators, while agreeing the constitutional order is at risk of unraveling, say voters were tricked and many who voted for Brexit had no idea that could put Britain outside the EU single market and customs union, something leading Brexit politicians promised wouldn't happen.
Mrs May was coming under intense pressure from Brexit-backing ministers and MPs to resist any outcome which would see the United Kingdom remain in a customs union, preventing it from striking new trade deals elsewhere in the world.
"I would like, in the coming hours and days, for Great Britain to reach an agreement on the way forward", he added. An earlier round of votes failed to produce a majority for any of eight proposals last week.
"There was nearly a majority in favour of a customs union with the EU".
May has ruled out all the ideas under consideration.
Linda McMahon Resigns As Head Of US Small Business Administration
The source with knowledge of the situation said McMahon has known America First Action's president, Brian Walsh, for years. The SBA provides support to small businesses through loans and monitors officials' compliance with federal contract laws.
The UK Parliament rejected May's Brexit withdrawal agreement for the third time on 29 March; the deal would have outlined the nation's exit from the EU. Over the weekend, a bloc of 170 Conservative members, including 10 cabinet ministers, wrote to May demanding that Britain leave the European Union.
This could involve her original deal brought back to the Commons for a fourth time, with MPs asked to choose between her deal and the new alternative on offer.
Public vote to prevent no deal (F): this new motion by Labour's Graham Jones and the Conservative Dominic Grieve says that if the United Kingdom is heading for a no-deal Brexit, this should be put to a public vote.
MPs from all parties will test support for other options during a second round of "indicative votes" on Monday.
Equally, there could be crisis if the government refuses to acknowledge parliament's preferred option.
"Since it took two and three-quarter years for the Government to get what it had negotiated defeated three times, it's a little bit harsh on Parliament, when it started the process last Wednesday, for not having immediately solved the problem in 24 hours", Mr Benn said.
But it has been roundly rejected by lawmakers on both sides of the Brexit divide.
Auger-Aliassime makes history, sets up Isner semi in Miami
He and Boric exchanged baseline rallies throughout the opening set and Felix was often seen taking charge. The stunning win took Auger Aliassime's career record against top-20 opponents to an astonishing 5-0.
But the Conservatives are anxious that could hand power to the opposition Labour Party.
Meanwhile, it was confirmed that senior ministers will meet in Cabinet for five hours on Tuesday - the first three hours in a "political" session in the absence of civil servants - to discuss the way ahead, amid speculation about possible resignations, a general election or change of Tory leader.
The cabinet is divided over whether the government should follow parliament's lead if a majority is found for a customs union.
Standard & Poor's said in an update Monday that a disorderly Brexit would "adversely affect income levels and growth prospects, as well as government finances".
"I think the deal is the right way to do that".
May is also facing mass calls from her own MPs to quit immediately as leader of the party - and country - rather than wait until the divorce phase of Brexit has been resolved, as promised.
The chief executive of industrial manufacturer Siemens U.K. implored lawmakers to unite around a compromise deal, saying "Brexit is exhausting our business and wrecking the country's tremendous reputation as an economic powerhouse".
Barty blasts past Kontaveit into biggest final of career in Miami
Long rallies, short rallies, Federer was in control and in a comfort zone against the Medvedev who is 14 years junior. Tomorrow in the semifinals, Isner will take on the Canadian phenom Felix Auger-Aliassime who continues to bust out.