Anti-Brexit protesters have gone online to vent their frustration at the chaotic process.
As of Friday morning, 5.9 million people had signed the petition, making it the most popular to have been submitted to the parliament website.
The petition calling for a people's vote continued to grow as Prime minister Theresa May sought fresh approval from MPs for her withdrawal agreement.
Friday's debate and vote, however, is unlikely to be a political declaration on the way the future EU-UK relationship will work, leading to criticism from the Labour party that it would lead to what they called the "blindest of blind Brexits".
Speaker John Bercow, previously sceptical of the Brexit divorce deal, eventually gave MPs the go-ahead to debate the plan Friday, despite parliament already rejecting it, twice.
"The motion is new, substantially different," Bercow told parliament.
Brexit: the deadline that wasn't. What happens now?
Anxious EU leaders last week offered Britain a Brexit extension until 22 May. But it is conditional on parliament voting through the Prime minister's deal by Friday 29 March, the day Britain was originally scheduled to leave the bloc.
Parliament's failure to pass the pact could result in a feared "no-deal Brexit" scenario on 12 April.
Retailers are warning that shelves in stores could be empty in the event of a no deal because Britain relies on the EU for imports. They also say EU tariffs could drive up the price of products.
No laughing matter
With no clear way out of the Brexit deadlock, the pound dropped on Thursday, despite May's dramatic pledge on Wednesday to quit in order to save her deal.
Her promise won over some likely contenders for her job, including Boris Johnson. However, parliament still rejected all eight of her options for a last-minute Brexit fix after several hours of debate.
On Monday, 1 April, parliament will be asked to debate again on how to fix Brexit. And for Leave campaigners it will be no laughing matter.