If her deal is voted down, Mrs May has vowed MPs will get a chance to vote the following day on whether to leave with no deal.
Then on March 14, there will be a vote on asking the EU to delay the deadline.
French President Emmanuel Macron said today the EU would agree to extend the Brexit deadline beyond March 29, as long as Britain has a good enough reason to do so.
But some business chiefs have said a delay just “prolonged the lack of clarity”.
Aston Martin Chief Executive Andy Palmer said to Reuters: “I would categorise it as a further annoyance.
“You’re holding that contingency stock for longer which means that your working capital is tied up for longer.”
What will happen if Theresa May delays Brexit?
At the moment, the UK will leave the EU on March 29, regardless of whether Mrs May has a deal or not.
But extending Article 50 will give Parliament more time to finalise a deal on the future relationship between the UK and the EU.
The UK doesn’t need permission from EU chiefs to withdraw Article 50 and stay in the EU.
But Mrs May will have to go to Brussels to ask EU officials and all 27 EU countries to agree on an extension.
If the EU does agree to this, the next date that the UK could leave is April 18.
This is also Maundy Thursday and is the day when the European Parliament will stop voting on issues before it has a break ahead of May’s European elections.
Another option for the Brexit date is June 23, the third anniversary of the EU referendum.
There have also been reports of a delay to Brexit until 2021.
But this will not go down well with the majority of the public, as it would be five years after people voted to leave the EU.