A petition calling on Theresa May to cancel Brexit by revoking Article 50 has attracted more than half a million signatures.
Parliament’s petitions website crashed on Thursday morning because of the high volume of traffic.
It comes as the prime minister heads to Brussels to ask the EU for a delay to next Friday’s Brexit date.
Foreign Secretary Jeremy Hunt told BBC Radio 4’s Today revoking Article 50 was possible but “highly unlikely”.
Commons leader Andrea Leadsom said she had been made aware of technical problems with the petition site – but she dismissed the petition as not being on the same scale as pro-Brexit vote in the 2016 referendum.
“Should it reach 17.4 million respondents then I am sure there will be a very clear case for taking action,” she told MPs.
She added: “It’s absolutely right that people do have the opportunity to put their views and that can then spark yet another Brexit debate.”
In December, the European Court of Justice ruled that the UK can unilaterally revoke Article 50 of the Treaty of the European Union.
This means the UK can decide to stay in the EU without the consent of the 27 other member states.
Few MPs have mentioned this as a potential option so far.
The petition currently has more than 700,000 signatures – above the 100,000 threshold that means it will be considered for debate.
Margaret Anne Georgiadou, who started the petition, told the BBC: “I became like every other Remainer – very frustrated that we’ve been silenced and ignored for so long.
“So I think now it’s almost like a dam bursting, because we’ve been held back in a sense – it’s almost like last chance saloon now.”
She said the petition “didn’t do very well for a week”.
“I nearly gave up but then I contacted a lot of people and it took off,” she added.
In January, MPs debated whether the UK should leave the EU without a deal, after a petition calling for that got 371,673 signatures.
MPs have been sharing the revoke Article 50 petition on social media, including Lib Dem Brexit spokesman Tom Brake, who said Mrs May’s “cliff-edge ultimatum” had led “hundreds of thousands” to sign.
Pete Wishart, who was among a number of SNP MPs who shared the petition, called on the public to sign and “end the madness”.
And Labour MP Neil Coyle urged the public to sign.
But Conservative MP Andrew Bowie said the only way to rule out a no-deal Brexit “at all” was to back the prime minister’s deal.
A House of Commons spokesperson said the site crashed on Thursday morning because of “a large and sustained load on the system”.
It briefly went back online, before disappearing again, with a note saying it was “down for maintenance”.
The petition reads: “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.”
Will the petition change anything?
By political reporter Brian Wheeler
Petitions on the Parliament website rarely lead to a change in the law.
They are not even guaranteed to lead to a debate in Parliament – they only get considered for debate if they reach 100,000 signatures. The petitions committee rejects them if it believes the UK government can’t do anything about the issue.
But what petitions can do is put an issue on the political radar – and that is what appears to have happened with the petition to revoke Article 50.
It was previously something of a taboo subject at Westminster.
Even the most ardent anti-Brexiteers know it would be political suicide for any prime minister to overturn a referendum result without going back to the people.
But some Remainer MPs are now calling on social media for the government to do just that.
The government will have a third try at getting MPs to back Theresa May’s EU withdrawal deal in a Commons vote next week, but only if it thinks it has enough support to win.
At the same time, a cross-party group of MPs will try to give Parliament control of Brexit by allowing a series of “indicative” votes on alternatives to the PM’s deal.
Jeremy Hunt insisted MPs only had a “limited” range of options “if we are in the same situation this time next week”.
He told BBC Radio 4’s Today programme: “Parliament could vote to revoke Article 50, which is cancelling the Brexit process. I think that’s highly unlikely.”
He said the other, more likely, options were leaving without a deal, or having a longer extension granted at an emergency EU summit, but with “onerous conditions”.
“The choice that we have now is one of resolving this issue or extreme unpredictability,” he said.