But, if faced with the threat of a calamitous no-deal Brexit, and following a narrow Commons defeat, Mrs May might fancy testing their resolve and seeing if she can win some cosmetic changes to appease enough MPs to win a second vote.
The prime minister said while there was "broad support" for many key aspects of it, there remained "widespread and deep concern" about the Northern Irish backstop.
On Monday, responding to the prime minister in the House of Commons, Corbyn did not specifically raise the possibility of a no-confidence vote - but he asserted that confidence in May's negotiations is flagging around the United Kingdom. Brexit is not on the agenda - instead the EU's long-term budget, single market, migration and external relations are up for discussion - but should the vote not go Mrs May's way, she could look to secure concessions in Brussels.
In the wake of reports that the Brexit vote had been called off, sterling fell 0.4 percent against the U.S. dollar to $1.26, the Press Association reports.
He said: "The Government has decided Theresa May's Brexit deal is so disastrous that it has taken the desperate step of delaying its own vote at the 11th hour".
May will make a statement to parliament on Brexit on Monday afternoon, House of Commons Speaker John Bercow's office announced, and she is then expected to confirm her plan to shelve the vote and set out the reasons why.
The withdrawal agreement has been endorsed by European Union leaders but now needs Parliament's backing. Critics say it could leave Britain tied to the European Union indefinitely, unable to strike new trade deals around the world.
In a stinging statement Monday to the House of Commons, May reminded lawmakers that any Brexit deal would require compromise.
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Meanwhile, rebel lawmakers in May's party said she had to go.
Earlier, the EU's top court had ruled on Monday that Britain could unilaterally reverse its decision to leave, easing concerns about Britain crashing out of the bloc in March without a deal.
Labour leader Jeremy Corbyn said the decision to postpone the vote was a sign of weak leadership from Mrs May.
"As President Juncker said, this deal is the best and only deal possible".
Irish Prime Minister Leo Varadkar ruled out reopening negotiations around the backstop, which is created to keep the Irish border open following Brexit.
May said she would hold talks with European Union leaders ahead of a summit in Brussels on Thursday and Friday, seeking "further reassurances" over the backstop. At least 104 Tory MPs have spoken out against it, as has Labour and the Tory's minority government partner the DUP. "This shambles can't go on - so how about it?"
Whatever new government emerges would have little time to solve the Brexit conundrum before March 29.
The Labour Party was urged by other smaller opposition parties to trigger a vote of no confidence in the government but said it would not act right away. It is far from clear whether or how Britain could organise a new referendum, notably given the short time left until Brexit.