Or does she tie herself to the mast of Morgan/Baker, knowing it is the route to a no-deal Brexit and the probable collapse of her government?
And Mr Johnson raised hopes of the amendment winning a majority in Tuesday evening's votes by tweeting: "If the Prime Minister indicates in the debate that she will be pressing Brussels to reopen the Withdrawal Agreement to make changes to the backstop, I will gladly support the Brady amendment".
The European Research Group, led by Jacob Rees-Mogg, said they want the government to table its own amendment that would commit to reopening the withdrawal agreement - the part of Mrs May's deal that lays out how the United Kingdom will leave the EU - to remove the backstop.
Shadow Brexit secretary Sir Keir Starmer said the plan "will allow Parliament to fill the void of leadership left by the Prime Minister".
The EU has repeatedly insisted it will not renegotiate the backstop arrangement, which is created to protect the border between Northern Ireland and the Republic of Ireland and prevent harming the Good Friday Agreement.
It is reportedly backed by members of both the Remain and Leave camps of the Conservative party.
Weather: Met Office issues snow warning
A yellow warning for snow and ice is also in... "If you must travel, pack a blanket, shovel and food in case you get stuck". We also reported how another band of snow will sweep in from the Arctic on Thursday, sparking another Met Office warning.
If the revised backstop arrangements are not accepted by the European Union, the United Kingdom would ask the bloc to accept the extended transition period and the country would prepare to leave the European Union on World Trade Organization (WTO) terms after December 2021.
Leading Conservative Brexiteers indicated they may not support "alternative arrangements" to keep the Irish border open, while the DUP - which props up Theresa May's minority Government - called on the Prime Minister to "face down the stubbornness of Dublin and Brussels".
"What a cunning plan", one European Union official is said to have remarked sarcastically, while an European Union diplomat was reported to have said, "This is just nonsense", according to The Guardian.
The so-called "Malthouse" alternative, negotiated by ERG leaders Jacob Rees-Mogg and Steve Baker and Tory Remainers including Nicky Morgan Stephen Hammond, has also been endorsed by Theresa May's allies in government, the DUP. They call for the contentious Irish backstop to expire by December 2021 or be removed from the Brexit deal altogether.
"We have seen the German economy weakening, we have seen the French economy weakening", he said.
An EU official also confirmed to the Guardian that such a response could be expected.
European Union rules out renegotiation of Brexit withdrawal agreement
If passed it could serve as a first step toward a compromise - known as the Malthouse plan - being discussed by the Cabinet today. Speaker of the House of Commons John Bercow will announce Tuesday which amendments have been selected for debate and vote.
While MPs will vote on May's plan B (criticised for its close resemblance to plan A), that vote is only to confirm that she has in fact got a plan, regardless of what politicians think of it. The PM was also willing to give the parliament another opportunity to vote for the Brexit deal as soon as possible. "The problem with the Brady amendment is that it does not spell out what they are".
Amendments that could alter the path of Brexit altogether are what really matter.
Tabled by Sir Graham Brady, the chairman of the backbench 1922 Committee, Mrs May said approving it would give her a clear mandate to demand changes from Brussels to the Withdrawal Agreement. That said, the next step in the Brexit process will depend on how the votes turn out later so we could either see a significant change to the current arrangement or it could lead to no changes at all.
Labour leader Jeremy Corbyn says it is "inevitable" that the government will have to delay Brexit.
But Ireland's Mr Coveney reiterated that the backstop was crucial in preventing a hard border and told the Press Association that "peace and the Good Friday Agreement are more important than Brexit".
She said that the Malthouse plan - to redraft the "backstop" and possibly leave the European Union without an agreement - was "a serious proposal that we are engaging with sincerely and positively".
Singer James Ingram Passes Away From Brain Cancer at Age 66
One of those hits Ingram had a hand in was Michael Jackson's "P.Y.T." which he and Quincy Jones co-wrote. Ingram was also nominated for Academy Awards in back-to-back to years for best original song.