But she refused to rule out a no-deal Brexit, and insisted that there was no majority in the House of Commons for a so-called People's Vote.
May will focus on changing the Northern Irish backstop, an insurance policy to ensure no return to a hard border between the British province and Ireland.
In fact, the biggest news in her remarks was the announcement that the 3 million European Union citizens living in Britain would not need to pay a planned 65 pound ($84) fee to apply for residency status after Brexit.
Jim Shannon, a lawmaker from the Democratic Unionist Party which props up May's minority government but opposes her Brexit deal, said it could be willing to support the agreement she has reached with Brussels if the backstop were time-limited.
"You´ve got a Leave population and a Remain parliament", International Trade Secretary Liam Fox, one of the senior Brexiteers in May´s cabinet, said on Sunday.
"Our amendment will allow MPs to vote on options to end this Brexit deadlock and prevent the chaos of a no deal".
But as MPs continue to row over how best to deal with Brexit - and even whether to go through with it at all - all sides would do well to heed the monarch's words in her recent Christmas message as the debate becomes ever more heated.
There were signs some Brexiteers could reluctantly back Mrs May's deal amid concerns a cross-party grouping of MPs are plotting to impose a "softer" Brexit - or derail it altogether.
"Parliament has to show some responsibility and do something hard and say well if the government needs more time, then we have to give it to them", said Cooper.
One of those legislators, Labour's Yvette Cooper, said May was shirking her responsibility to the country by refusing to take "no deal" off the table.
The formula of "keeping all options on the table" sticks to the compromise agreed by the Labour Party past year that has enabled Corbyn, a lifelong Euroskeptic, to hold off demands from rank-and-file members and lawmakers to support a second referendum.
Cristiano Ronaldo Wins The Italian Super Cup For The Squad
He scored after the Milan defense was caught napping on the 61st minute, nodding on a punt from Miralem Pjanic. The win took the Turin side to a record eight Supercoppa titles, one more than Tuesday's opponents Milan .
"But, a no-deal Brexit will clearly, clearly put most of these things in risk and this is something that we need to address in the framework of our contingency planning with Ireland".
The 650-seat parliament is deeply divided over Brexit, with different factions supporting a wide range of options including leaving without a deal, holding a second referendum and seeking a customs union with the EU.
While this amendment is unlikely to pass as few if any Tories will support a motion bearing Corbyn's name.
If no agreement can be ratified before March 29, the United Kingdom will lurch out of the European Union with no deal, risking dire economic consequences, including a recession, and potentially a 25% fall in the value of the pound, according to British authorities.
"This is a fair deal that 27 members strongly support so I would really not touch", he said.
After May sets out her plans for the way ahead, lawmakers are set to table a series of amendments, to be voted upon on January 29.
They oppose the arrangement because, in order to keep the border frictionless, Northern Ireland would be required to follow some European Union rules and regulations. "The government should be reopening those red lines", she said.
He said if the backstop were removed then most of the opposition to the deal from eurosceptics in her party would be removed.
But while May said she would "ensure that members have the chance to make their views known", she has not altered her approach in response to numerous views that have already been expressed.
May´s Downing Street office has called them "extremely concerning".