The Government is obliged to hold a meaningful vote on the Prime Minister's Brexit deal after a successful 2016 legal challenge by activist Gina Miller, so while the Prime Minister may be able to defer the vote she is not able to cancel it.
The Prime Minister's comments came as her Government was hit by another resignation over the Brexit plan.
EU leaders have rejected the prospect of renegotiating the withdrawal agreement itself but European sources speaking privately say tweaks in the accompanying declaration on post-Brexit ties might be possible.
UK Prime Minister Theresa May ended up evoking laughter from the assembled members of parliament as she addressed the House of Commons after cancelling the vote on her Brexit deal.
The report that May could cancel the vote came just hours after the top European Union court ruled that Britain could cancel its notice to leave the bloc, which it is due to exit on March, 29.
A defeat for the deal on Tuesday could see Britain crashing out of the European Union on March 29, the date for Britain's exit, with no agreement in place - an outcome that could spell economic chaos.
That is the view among some senior officials inside the government, on both the pro- and anti-Brexit wings of the Conservative Party.
For different reasons, over 100 ruling Conservative MPs have declared their intention to vote against the agreement, besides the opposition Labour, Liberal Democrats, Scottish National Party and the Northern Ireland-based Democratic Unionist Party, which is propping up the minority May government. "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 eleventh hour".More news: Virat Kohli savours 'special' India win as Tim Paine hails Australia's fight
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Such an alternative "seems plausible, not just in terms of the country but in terms of where the MPs (lawmakers) are", she added, although "nobody knows if it can be done".
"It is clear that while there is broad support for numerous key aspects of the deal, on one issue, the Northern Ireland backstop, there remains widespread and deep concern", May said.
Last week Brady had publicly urged the premier to drop her plans for a vote, amid opposition to the so-called Irish border backstop.
The prime minister could face demands to head to Brussels and attempt to extract concessions before putting the deal to a second vote by parliament.
Mrs May said she believed she could still get the deal through if she addressed MPs' concerns and that what she meant to do in the next few days.
"The United Kingdom is free to revoke unilaterally the notification of its intention to withdraw from the European Union", the court said, in response to a suit from a group of Scottish politicians.
"We voted very clearly", Environment Secretary Michael Gove, an influential cabinet Brexit supporter, told BBC radio after Monday's decision.
But EU leaders have insisted the divorce agreement is final and not renegotiable.