Despite a growing clamour holding a new vote is a complicated and lengthy process, requiring new laws, agreement on a question - and a delay to Brexit day on March 29.
Theresa May has insisted repeatedly that a new referendum would betray Leave voters in 2016 and will not happen on her watch.
But Parliament could force the PM into the decision - prompting Nigel Farage to tell Leave campaigners to prepare for another vote.
A new referendum would take almost six months - at least - to pass the necessary laws, establish campaigns and actually have the battle at the ballot box
Why do people say there needs to be a second referendum?
Theresa May's Brexit deal has no majority in Parliament - and it is not clear any other deal has a majority either, even if one could be negotiated.
Passing the question back to voters is seen by some as a way to end the impasse and give a clear instruction to politicians on what to do.
Some campaigners also say the 2016 referendum was not an informed choice because too many of the implications of Leave were unknown.
What do critics think?
Many people - led by the Prime Minister herself - say a new vote on Brexit would betray the people who voted Leave in 2016. They insist there was a clear order from the public to Leave the EU and politicians must follow it, working out the details for themselves.
Unionists also complain that accepting a new referendum on Brexit would pave the way for another referendum on Scottish independence, threatening the future of the UK.
Some politicians also feel it would simply reopen the wounds from the 2016 battle without really deciding anything more clearly.
What needs to happen for a referendum to happen?
Parliament would need to pass a new law for a referendum to be held. This process alone would take weeks and would likely be very controversial.
Before that can even happen, for political reasons there would probably have to be some kind of moment creating a