His party wants a public vote once the terms of the UK’s departure from the EU are known.
Nicola Sturgeon has said a second ballot could become “irresistible”, but has stopped short of fully endorsing one.
Addressing the Scottish Lib Dem conference in Aviemore, Sir Vince said support for the campaign to stop Brexit was building.
He said the UK Government’s deal with the EU was “unravelling”, citing problems resolving the Irish border issue, and claimed the recent Windrush scandal had exposed the “potential nightmare” of managing EU migration.
“The proposals for the Irish border have been comprehensively rejected out of hand, the chaos around immigration shows that the registration of three million people is potentially a nightmare, and the Commonwealth has shown very little interest in the free trade proposals,” he said.
“I think what’s happening on the back of all this is a recognition that we have to have a public vote on the final deal.”
Sir Vince told supporters that the House of Lords was “almost certainly going to come forward with a referendum on the final deal”.
“Each of the political parties will have to stand up and be counted,” he said.
“A key uncertainty is where the SNP fit into all of this.
“They have got to declare their position and they have got to make a choice.
“Are they concerned with narrow tactical party advantage or are they concerned with the wider national interest?”
SNP MSP Rona Mackay said the Lib Dem leader would rather attack the SNP government over Brexit than the Conservatives and Labour.
“It is Theresa May and Jeremy Corbyn who both want to drag Scotland out of Europe against our will - not the SNP,” she said.
“They (the Lib Dems) should be joining our fight to keep Scotland in the Single Market, backing jobs, living standards and our economy - and keeping the pressure on the Tories who have no mandate here.”
Sir Vince also used his speech to attack the UK Government’s decision to carry out air strikes in Syria without consulting Parliament.
He said: “We do accept that there are circumstances where governments do have to intervene.
“On this particular occasion, the emphasis of our campaigning was on making sure there was a proper debate in Parliament.
“This wasn’t just a pedantic, procedural argument, it was actually about demanding that if we intervene in a military way the government of the day has to get the country behind it.”
His comments came after party members backed an emergency resolution calling for MPs to have a vote on military action.
Elsewhere at the conference, delegates also voted in favour of lowering the minimum age for candidates standing in Scottish Parliamentary elections from 18 to 16.
The move would bring the candidacy age in line with the Holyrood voting franchise.