Prime Minister Theresa May has twice failed to win the endorsement of Parliament for the Brexit deal she agreed with EU leaders in November.
The leaders of the other EU nations have agreed to delay Brexit from March 29 until May 22 to see if she can finally win the support of MPs.
But should she fail, Mrs May will have until just April 12 to come up with a new approach.
The petition on the Parliament website states: “The Government repeatedly claims exiting the EU is ‘the will of the people’.
“We need to put a stop to this claim by proving the strength of public support now, for remaining in the EU. A People’s Vote may not happen - so vote now.”
Parliament considers all petitions that get more than 100,000 signatures for a debate, thus far the call to ‘Revoke Article 50 and remain in the EU’ has attracted the support of over five million people.
Across Lanarkshire’s seven constituencies alone more than 45,000 people have so far signed the petition.
In the House of Commons last week Motherwell and Wishaw MP Marion Fellows brought up the petition with Leader of the House Andrea Leadsome.
However, Ms Leadsom basically dismissed it, stating: “Should it reach 17.4 million respondents then I’m sure there would be a very clear case for taking action.”
Afterwards Mrs Fellows said: “The UK Government is so determined to take Scotland off the edge of a cliff that they are completely unwilling to listen to the public.
“Theresa May has failed to satisfy the far right of her party, the DUP whom she bribed for votes, Parliament or the public. Both the UK government and the British political system has failed entirely since the beginning of the Brexit process. It will be people across the UK who will pay the price.”