While there's genuine anger in the European Union at the way May has handled things since the deal was struck in November, both sides are complicit in the high-stakes strategy of running down time, one European Union diplomat said.
In the past, Corbyn repeatedly called for a general election should the prime minister fail to get a deal approved by Parliament.
May told ministers that parliament, which last month roundly rejected her Brexit deal, would not vote on a revised deal this week as she needed more time to negotiate with the EU.
"The talks are at a crucial stage", May will say, according to extracts from her statement to parliament released in advance by her Downing Street office.
Critics of the backstop say it could leave Britain subject to European Union rules for years after leaving the bloc or even indefinitely. "We now all need to hold our nerve to get the changes this house requires and deliver Brexit on time", May said in her statement at the House of Commons.
Parliament is to hold a debate on Brexit on February 14, but with just 45 days until Britain leaves the bloc it is not expected to change the course of the exit process, and no date has been set for another vote to approve or reject May's deal.
The measure, known as the backstop, is a safeguard that would keep the United Kingdom in a customs union with the EU and removes the need for checks along the border until a permanent new trading relationship is in place.
Yet again, this wouldn't amount to binding legal assurances but they are merely political commitments created to offer some leeway in the current Brexit withdrawal agreement.
The EU has ruled out reopening the withdrawal agreement but signalled that changes might be possible to the political declaration that sketches out the UK's future relationship.
Brexiteer MPs in her Conservative Party are particularly unhappy with the so-called backstop provision meant to keep the border with Ireland free-flowing.
"I believe we can reach a deal that this House can support", Mrs May told parliament.
Senior negotiator Olly Robbins was reported to have been overheard in a Brussels bar saying Theresa May planned to wait until the end of March before confronting MPs with a choice between her deal or a lengthy delay to Brexit.
Commons Leader Andrea said on BBC radio that May was not simply "running down the clock" until March 29.
She also said that normal parliamentary treaty-ratification processes, which also have to be completed before Brexit day, might be suspended or truncated in order to get the withdrawal agreement over the line before March 29.
"She is playing for time, and playing with people's jobs, our economic security, and the future of our industries", he said.
The British government denied on February 13 it was secretly plotting to force MPs into a last-minute choice on Brexit between a rejigged deal or a lengthy delay. On Monday, figures released by the Office for National Statistics showed the economy shrunk by 0.4 per cent in December and that it grew by 1.4 per cent a year ago, the slowest rate since 2009.