Sir Vince Cable has insisted it is "perfectly plausible" that he could become the next prime minister.
The Liberal Democrat leader said politics was in a "remarkable state of flux", with both major parties divided.
On day two of its conference, the party leadership saw off a challenge to its policy on a second EU referendum.
Members backed the idea of an "exit from Brexit" poll, although former leader Tim Farron warned them not to treat Leave voters "like idiots".
Asked how Brexit could be stopped, given that Article 50 has been triggered and both the Tories and Labour are opposed to another vote, Sir Vince said "sensible" figures within Labour were coming round to the idea.
Although public opinion had not changed much since the Brexit referendum, he told the BBC's Andrew Marr show this would happen once the economic reality of withdrawal from the EU sank in.
He argued that the public should be given a second chance to settle the issue once and for all, with an option to stay put.
Despite winning four more seats in June's general election, where a second referendum was the centrepiece of its campaign, the Lib Dem vote share fell to 7.4%.
Pushed on whether it was realistic to go from such a low level to winning a majority, Sir Vince - who served in the coalition government for five years - said it was "perfectly plausible".
The Lib Dems, he suggested, were well placed to capitalise on the "open civil war" within the Conservative government and the "suppressed" divisions within Jeremy Corbyn's Labour party.
He said: "As leader of the third UK party my job is to be the alternative PM.
"It's possible...that we could break through. If British party politics starts to break up, if traditional structures start to break up, that could well happen.
"We are extremely well positioned - with moderate sensible policies, a good track record in government, we have government experience, experience at local government level.
"I think what you may find is a big shift of opinion in our direction - so I am very confident talking about being an alternative PM."
Lib Dem activists overwhelmingly endorsed the leadership's policy of seeking another referendum on the final Brexit deal, although not without dissent from several activists, including some from heavy Leave-voting areas.
One member from Sunderland, which voted by a margin of 61% to 39% to leave, warned that the idea of staging another referendum was a "dead horse the party should stop flogging".
Another said that the idea had proved "toxic" to voters during the election campaign and urged MPs and peers in Westminster to "end their love affair" with the concept.
But senior figures rallied behind the party leadership, with former leader Sir Menzies Campbell saying the odds of the Lib Dems forming a government before the conclusion of Brexit talks was remote and the party's energies were better directed at "winning a referendum in association with other parties".
While backing the policy, Tim Farron warned his party against "lecturing the country" about the issue.
The only way to "save" the UK from the damage Brexit would do would be to "change the hearts and minds of the people", he told activists.
Amid calls for more radical thinking from the party, the Lib Dem leader has also announced a review of tuition fees policy, saying none of the parties is in "a good place" over the issue.
It comes amid unconfirmed reports that the government is looking at ways of reducing the financial burden on students - either potentially by reducing the £9,250 maximum fee chargeable by universities or the 6.1% interest rate on re-payments.
Sir Vince said the party's U-turn on tuition fee increases in 2011, while in coalition with the Conservatives, had caused lasting damage and a new approach was needed.
He said the current system, in which there are no upfront costs and graduates do not have to pay anything until they earn £21,000, had many good elements.
Meanwhile, the party's former leadership contender Norman Lamb has said he will stand down as Lib Dem health spokesman to concentrate on his new role as chairman of the Commons science and technology committee.
The BBC's political correspondent Andrew Sinclar said Mr Lamb has been known to be unhappy with aspects of party policy, particularly over Brexit, but that the MP insisted there was no rift with his party leader.