May was also lashed by the resignations last week of three prominent Tories who want to remain in the European Union and fear May is about to drive Britain over a cliff-edge into a disastrous "no-deal" Brexit.
But Corbyn also said Labour would oppose any agreement based on the "overwhelmingly rejected" one negotiated by Prime Minister Theresa May's government.
May has steadfastly argued that she must keep the prospect of Britain crashing out the bloc without an agreement on March 29 on the table in order to wrest essential concessions from Brussels.
The extension of Brexit deadline is not expected to be a protracted delay, as Mrs May said she prefers it to be "the shortest possible".
Voters narrowly approved the June 2016 referendum to pull Britain out of the EU.
Jeremy Corbyn's amendment will seek support for his party's five Brexit demands.
Shadow Brexit secretary Sir Keir Starmer said that if Labour's Brexit proposals did not get through Parliament "we, the Labour Party will either put down ourselves, or support an amendment, in favour of a public vote".
Labour is not yet making clear what its proposed referendum would be on.
The rebel ministers were all backing a proposed parliamentary amendment that would force May to set a new Brexit date if she fails to get better terms on the disputed issue of the border between Northern Ireland and European Union member Ireland.
Amtrak Train With 183 Passengers Stranded In Oakridge Amid Snowstorm
By Tuesday morning, at least 30cm had accumulated, the weather service said. "Please send help if possible", she said. Despite the hard circumstances, she noted that the crew had been "very professional" and were working tirelessly.
May wants to change the deal to reassure British lawmakers that the backstop would only apply temporarily.
The EU is adamant that the legally binding withdrawal agreement can't be changed, though the bloc's negotiators are holding talks with U.K. Attorney General Geoffrey Cox about potential tweaks or additions around the margins.
The bleak government assessment of the no-deal impact found that customs checks could cost business £13bn a year in a no-deal scenario and warned that there was "little evidence that businesses are preparing in earnest".
The Bank of England also forecast in November that a no-deal Brexit in March would cause the United Kingdom economy to shrink by about 8% within a year, the worst drop the country has seen since the 1920s.
And Lucy Powell said she "remained to be convinced" on supporting a second referendum, predicting around 25 of her colleagues would not vote for it.
A number of British lawmakers are seeking to wrest control of the process away from government and are looking to get support for an amendment that would require May to seek an extension to the Brexit date if Parliament fails to back her deal.
"I don't see how businesses can plan, I don't see how public services can plan and I think it's just deeply damaging", Cooper told the BBC.
While no final decision has been taken, putting off the U.K.'s scheduled withdrawal from the European Union would be a huge political gamble.
Tusk said he told May that "no matter which scenario, all 27 (EU countries) will show maximum understanding and good will".
However, May insisted she could deliver on the set date.
Carolyn Fairbairn, the Confederation of British Industry's director general, said: "Delay can not simply be an extension of stalemate".