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".
The petition quickly passed the 100,000 threshold that means it will be considered for debate in Parliament.
It is currently heading towards 700,000 signatures, with more than 40,000 people signing it in the past hour.
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 salon 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.
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."
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 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.