With just over 100 days until Britain leaves the bloc on March 29, Brexit remains up in the air with growing calls for a no-deal exit, a potentially disorderly divorce that business fears would be highly damaging, or for a second referendum, Reuters wrote.
May pulled a vote on her deal on Monday after acknowledging it would be heavily defeated over concerns about the "backstop", an insurance policy designed to avoid any hard land border for Ireland but which critics say could bind Britain to EU rules indefinitely.
Two days later, she survived a plot to oust her from her those in her own party who support a hardline Brexit, showing the level of opposition she faced.
May herself has acknowledged that Britain's parliament appears deadlocked with no clear support for any option, with the small Northern Irish party that props up her government leading the criticism of her deal.
"Brexit is in danger of getting stuck – and that is something that should worry us all," Pensions Minister Amber Rudd wrote in Saturday's Daily Mail newspaper.
"If MPs (lawmakers) dig in against the prime minister’s deal and then hunker down in their different corners, none with a majority, the country will face serious trouble."
At a summit in Brussels, May's attempts to get legal assurances from the EU that the Irish backstop would only be a temporary measure was rebuffed with the bloc's other 27 leaders saying they would not renegotiate the treaty.
However, May insisted at the summit's conclusion on Friday that further clarification was still possible with German Chancellor Angela Merkel saying: "We want to be helpful".
Britain's Foreign Secretary Jeremy Hunt said parliament could still rally behind May's agreement with additional assurances and said such clarifications were likely because EU countries knew no deal would be a disaster for them.
"When the dust has settled, the only way we're going to get this through the House of Commons ... is to have a version of the deal that the government has negotiated," Hunt told BBC radio. "I don't think the EU could be remotely sure that if we don't find a way through this we wouldn't end up with no deal."