A no-deal Brexit is now more likely but can still be avoided, the EU's chief negotiator has said.
On Monday night, MPs voted on four alternatives to the PM's withdrawal deal, but none gained a majority.
Michel Barnier said a long extension to the UK's current 12 April exit date carried "significant risks for the EU" and that a "strong justification would be needed" before the EU would agree.
Theresa May is set for five hours of cabinet talks to tackle the deadlock.
MPs rejected a customs union with the EU by three votes while a motion for another referendum got the most votes in favour, but still lost.
The so-called indicative votes were not legally binding, but they had been billed as the moment when Parliament might finally compromise.
That did not happen, however, and one Tory MP - Nick Boles, who was behind one of the proposals - resigned the whip in frustration.
Brexit Secretary Stephen Barclay told MPs that if they wanted to secure a further delay from the EU, the government must be able to put forward a "credible proposition" as to what it would do.
One suggestion has been the possibility of a general election - but former foreign secretary Boris Johnson told BBC political editor Laura Kuenssberg that would likely "infuriate" voters.
Instead, Mr Johnson said he believed a new leader and "change in negotiation tactic" could "retrofit" the PM's "terrible" agreement with the EU.
Labour MP and chairman of the Brexit select committee Hilary Benn told BBC Radio 4's Today that a confirmatory referendum was the best solution.
"A good leader would be taking that decision and put it back to the people," he said.
"[The] fear is that the PM is not going to move an inch. That is why we are at a moment of crisis."
Speaking on Tuesday morning, Mr Barnier said: "No deal was never our desire or intended scenario but the EU 27 is now prepared. It becomes day after day more likely."