(CNN) British Prime Minister Theresa May was accused of leading the UK into a "national crisis" on Monday as she ignored pleas to abandon her widely-criticized Brexit plan.

May announced that she would reschedule a parliamentary vote on her Brexit plan during the week of January 14 -- less than 80 days before Britain is due to leave the European Union on March 29.

"I know this is not everyone's perfect deal. It is a compromise," May said. "But if we let the perfect be the enemy of the good, we risk leaving the EU with no deal."

Opposition leader Jeremy Corbyn accused the Prime Minister of "cynically running down the clock" until the UK leaves the EU by offering lawmakers "her deal or no deal." He added that May had been the architect of leading the UK into a "national crisis."

"A responsible prime minister would, for the good of this country, have put the deal before the House this week, so we can move on from this Government's disastrous negotiations," Corbyn told the House of Commons.

"It's clear the Prime Minister has failed to renegotiate her deal, failed to get any meaningful reassurances -- there is no excuse for any more dither or delay."

Corbyn accused May of leading the UK into a "national crisis."

As pressure for a new vote grew inside and outside a bitterly divided Westminster, May dismissed calls to change course and firmly rejected holding a second Brexit referendum. She said doing so would be a betrayal of the British people.

"Let us not break faith with the British people by trying to stage another referendum, another vote, which would do irreparable damage to our politics. Because, it would say to millions who trusted in our democracy that our democracy does not deliver," she told the Commons.

May also ignored calls from MPs to hold the parliamentary vote sooner, and described claims that a better Brexit agreement could be reached as "fiction."

"I know there are a range of very strongly-held personal views on this issue across the House and I respect all of them," May said.

"But expressing our personal views is not what we are here to do. We asked the British people to take this decision."

She also urged lawmakers to "not follow" Labour leader Corbyn into triggering a general election.

"And let us not follow the leader of the opposition in thinking what gives him the best chance in forcing a general election, for at this critical moment in our history we should be thinking not about our parties' interest but the national interest," May said.

Parliamentary vote called off last week

The Prime Minister abruptly called off a vote on her Brexit plan last week, after it became clear it would be defeated. She was then forced to fend off a leadership challenge from rebellious Tory MPs. The challenge failed, but left her weakened politically.

At a European Union summit in Brussels, May failed to secure guarantees that would satisfy her rebels.

Over the weekend, the Sunday Times reported that two of May's allies -- Cabinet Office Minister David Lidington and her Chief of Staff Gavin Barwell -- were preparing for a second referendum as "the only way forward."

Lidington is part of a group of senior ministers -- Philip Hammond, Amber Rudd, David Gauke and Greg Clark -- who believe a new referendum may be the only way to break the parliamentary gridlock, the newspaper said.

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New vote?

Months ago, a second Brexit referendum was widely seen as improbable, a last-ditch attempt by bitter Remain voters to undo a result they didn't like.

But support for a new poll -- and pressure from influential sections of the media and politics -- has been growing, especially as it has become increasingly clear the parliamentary math does not favor May's Brexit bill.

With Brexit due to take place on March 29, such an impasse increases the possibility of a "no deal" exit, which could crater the UK economy and even lead to fuel and food shortages , according to to predictions.

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One complication for supporters of a new referendum is that it would require an extension of the Article 50 process -- the legal mechanism by which the UK is leaving the EU. That process requires the UK to leave the EU on March 29, whether a withdrawal deal is in place or not. It can only be extended if Britain requests it, and the remaining 27 EU nations agree.

The opposition Labour Party favors a general election to break the deadlock -- although that could also require an extension of the Article 50 process. Labour has repeatedly threatened to call a vote of no confidence in May's government should her Brexit bill be defeated or further delayed, a move that could pave the way to a new election.

Should his party fail in its efforts to secure an election, Corbyn has committed to "all options," including a second referendum.

But he has been reluctant to wholeheartedly endorse calls for another referendum, fearful that it would cost the party support in areas of the country that voted in favor of Brexit.

The Liberal Democrats -- a minor opposition party previously in a coalition government with May's predecessor David Cameron -- have come out in favor of a new vote, but this has not translated into much of an increase in support.

On the right of the Labour Party, however, some pro-European figures have voiced strong support for a new vote. They include former leader Tony Blair, a longtime critic of Corbyn and a hugely divisive figure for Labour voters.

"It is perfectly clear neither the British people nor their Parliament will unite behind the Prime Minister's deal. That is why the government decided not to proceed with the vote," Blair said Sunday

"In these circumstances it is not irresponsible or insulting to put forward an alternative way to achieve resolution ... If (Parliament) can't reach agreement then the logical thing is to go back to the people."