"Brexit is not inevitable - it can and it must be stopped," Sir Vince Cable has told his party's annual conference.
The Lib Dem leader said 29 March next year - the date the UK is set to leave the EU - was "only a maybe".
He claimed there was a growing realisation that Brexit will be "costly and painful", particularly in a no-deal scenario.
And he urged Theresa May and Jeremy Corbyn to get behind the cross-party campaign for another referendum.
Mrs May has said there will not be another referendum "under any circumstances" and Mr Corbyn has said he would prefer a general election.
Sir Vince spoke for 45 minutes and received a standing ovation from the party faithful in the Brighton conference centre for what was a sombre, thoughtful address with few jokes.
Some of the loudest cheers came when he said Jeremy Corbyn should resign as Labour leader if he does not agree to demands from his own MPs and party members for a referendum on the final Brexit deal at their party conference next week.
"If Jeremy Corbyn will not say 'I will support a People's Vote and I will fight Brexit', Labour members should wave him goodbye," said Sir Vince.
"He is currently letting down the many people in Labour's heartland who now see Brexit for what it is. It's a Tory project, pursued for Tory ends, of which working people will be the main victims."
He described Tory Brexiteers like Jacob Rees-Mogg, as "fundamentalists" for which "the costs of Brexit have always been irrelevant".
He was due to say that "years of economic pain justified by the erotic spasm of leaving the European Union. Economic pain felt - of course - not by them by those least able to afford it."
However Sir Vince mangled the "erotic spasm" line that had grabbed most of the overnight headlines:
The Lib Dem leader took aim at what he described as Tory "chancers" like Michael Gove and Boris Johnson, who he said had only backed Brexit to further their own leadership ambitions.
He said Mr Johnson was a "real danger to Britain", comparing him with US President Donald Trump.
"He doesn't just resemble Trump - large, loud and blonde - he behaves more like him by the day.
"Their cynical disregard for the truth, their treatment of women, and their inflammatory divisive language make Boris and Donald the 'terrible twins of the rabid right'."
Mr Gove, on the other hand, was the "ideal man for a penalty shoot out - right to the last moment you never know which way he will go".
The Lib Dem leader, who has said he will step down when Brexit has been "resolved or stopped", has put the chances of another referendum at about "30%".
But he is talking to anti-Brexit Labour and Conservative MPs about how to get a second referendum, possibly by tabling a new bill or an amendment to legislation already going through Parliament, with proposed referendum questions.
He claimed Theresa May, who voted Remain in the 2016 EU referendum but has vowed to deliver on the will of the people, knows "deep down" that Brexit is a "bad idea" whose "time has gone".
He urged her to show "true leadership" by admitting that staying in the EU will be better than any deal she can get in Brussels.
"Instead of kowtowing to her enemies in the Conservative Party, she could lead her party and the country by opening her mind to a 'People's Vote' on the final deal", he said.
The Lib Dem leader also used his speech to set out a vision of a "liberal future" for Britain after the "Brexit nightmare" has been stopped, vowing to "restore a sense of fairness and opportunity to a country where both have been lost".
He set out plans, announced at the weekend, to set up a £100bn citizens' fund to spread the UK's wealth more evenly, paid for, in part, by abolishing inheritance tax and replacing it with a "levy on large financial gifts received over a lifetime".
The Lib Dems would also increase taxes on the wealthy, tackle homelessness, solve the housing crisis and combat racism, while controlling immigration, he said, referring to his "personal experience of racism" in the late 1960s.
"My wife and children were being denounced as people whose very presence here would lead to rivers foaming with blood. And I was thrown out of the parental home," he told his party conference.
Sir Vince also used his speech to set out plans to transform his party, which has 12 MPs and has languished in the opinion polls since being in coalition with the Tories, into a "movement for moderates" and open up its next leadership contest to non-MPs.
He said the party was still "very pale and very male", adding: "We must change that and keep growing."