The UK Parliament defeated a measure to hold a second referendum on Wednesday, turning down a chance to hold a people’s vote on the future of Brexit.

The decision came as part of Thursday’s vote on whether Parliament will ask the European Union to extend the Brexit deadline. Sarah Wollaston, a former Conservative member of Parliament (MP) who recently joined the breakaway Independent Group, put forth the amendment, which specifically requested a delay from the EU to put the question of Brexit — whether, or how, the UK will leave the EU — back to the public for a vote.

MPs voted against it, 85 to 334 — a huge loss that wasn’t all that surprising because even some referendum advocates argued that Thursday wasn’t the time to take up the issue.

Labour, the main opposition party, whipped its members to abstain from voting. Even strong backers of a second referendum, such as the main advocacy group, the People’s Vote campaign, were lukewarm about the vote on Thursday, saying MPs should simply focus on achieving a Brexit deadline extension. The group said the debate over the second referendum could come later, and supporters of a second referendum wrote an open letter explaining their decision to abstain.

“We do not think today is the right time to test the will of the House on the case for a new public vote,” a spokesperson for the group said in a statement earlier on Thursday. “This is the time for Parliament to declare it wants an extension of Article 50 so that, after two-and-a-half years of vexed negotiations, our political leaders can finally decide on what Brexit means.”

Voting for a #PeoplesVote. Where is the rest of the Labour Party? A few notable exceptions but... pic.twitter.com/pSP9C6wJDW — Layla Moran (@LaylaMoran) March 14, 2019

This was one of the first times Parliament has voted on an amendment that took up the question of holding a second referendum — and, depending on how things play out with the rest of Thursday’s votes — it probably won’t be the last.

A second referendum could offer the people another chance to vote on Brexit. But it’s not without its problems.

A second referendum has some strong advocates in Parliament in both the Labour and Conservative parties and among some of the more “Remain”-minded voters. British Prime Minister Theresa May has continued to reject the idea as undemocratic, insisting that the UK already made its decision during the 2016 referendum and that it’s her job to deliver on that result.

The People’s Vote campaign argues that it’s impossible to “undo democracy by having more democracy,” but another such vote is sure to be divisive, as the UK is still deeply split on the Brexit question.

Practical complications abound with a second referendum. It would certainly require a long-term extension of the Brexit deadline (estimates say about 22 weeks). It’s also not clear what questions would be asked in any such vote. The People’s Vote campaign is promoting a referendum offering a choice between May’s deal — the 585-page one — and the “current deal,” which is basically EU membership and the status quo. But some have suggested three options: no-deal Brexit, May’s deal, and Remain, which could potentially split votes, leading to an outcome few desire.

This debate is far from over, though. If the UK Parliament votes to postpone the Brexit deadline beyond March 29, which seems likely, members of Parliament will then have to figure out what they’re going to do with more time, provided the European Union agrees to an extension. Supporters of a second referendum will seize on that opportunity to build their case.