The pound fell to the lowest since June 2017 as market fears about a no-deal Brexit resurfaced after the report that May's vote will be delayed.
"This is yet another blow for companies desperate for clarity", said Carolyn Fairbairn, head of big business lobby the Confederation of British Industry.
Another official said the political declaration - the part of the Brexit deal that isn't legally binding - could be revised, but that changing the backstop arrangement itself would be a "step too far".
May faced a huge rebellion of her own Conservative MPs over the deal, primarily over a "backstop" clause created to keep open Britain's border with Ireland. May asked. "If the answer is yes, and I believe that is the answer of the majority of this House, then we all have to ask ourselves whether we are prepared to make a compromise".
May spoke over the weekend to European Council President Donald Tusk - who will chair an EU summit in Brussels on Thursday - and European leaders including Irish Prime Minister Leo Varadkar, amid signs she was seeking to tweak the deal to win over skeptical lawmakers. She has been humiliated by her own MPs.
It was not immediately clear whether the EU's 27 other members, which have a combined economic might six times that of the United Kingdom, would countenance changes which would convince her domestic opponents to support a deal.
In unusually strong language, the CBI, the large employers' body, said that Britain "risks sliding towards a national crisis" unless a deal was agreed soon.
"Our country deserves better than this".
May pulled the vote set for Tuesday after repeated warnings from MPs that the scale of the expected defeat could sink her government.
May could also be ousted by MPs from within her own Conservative Party and British media are full of speculation on potential contenders.
The delay was confirmed during an emergency conference call of Cabinet ministers at 11.30am and quickly leaked - minutes after a spokesman for the Prime Minister had insisted to journalists that the vote was going ahead.
Any assurances May secures from the European Union over the contentious backstop will be "completely irrelevant" if they are not included in the withdrawal agreement, lawmaker Jacob Rees-Mogg, a leading Brexit supporter, told reporters.
"We can not continue like this".
There are also voices calling for opposition leader Jeremy Corbyn to bring forward a motion of "no confidence" in the prime minister.
A small Northern Irish party which props up May's Conservative minority government called the situation a shambles.
Theresa May chose to pull the parliamentary vote on her Brexit withdrawal agreement because she knew she would lose.
She said she had "no doubt this deal is the right one" but promised to seek "additional reassurance" from the European Union over a controversial provision on Northern Ireland.
If that were to go ahead, and if enough MPs from Labour, the Scottish Nationalist Party and others agree, the government would fall and a general election would be triggered.
A no-deal Brexit, though, is seen as so disruptive that parliament would be under strong pressure to block it.
Adding another twist to the scenario, the European Court of Justice-the bloc's top court-determined that it would be legal for the U.K.to cancel Brexit altogether without requesting the permission of the rest of the EU.
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