David Steel once told a Liberal conference to “go away and prepare for government”. They went away and remained in opposition. Vince Cable once said that he could imagine himself becoming prime minister. Which is where that idea stayed: in his imagination. Nick Clegg did take them into government during the coalition years, an experience that ended with the Lib Dems losing all but eight of the 57 MPs they started with five years earlier.

So they have had fair warning about the perils of dreaming of breakthroughs. They usually don’t come true. On the rare occasions when they do, the consequences for the party can be terrible. But dream they always will and never more so than now.

Jo Swinson, their new leader, calls herself “a candidate for prime minister”. While that line rings ridiculous in non-Lib Dem ears, it generates plenty of applause from activists intoxicated by the party’s recent successes and the swelling of their membership to more than 120,000. The Bournemouth conference is the most buoyant Lib Dem gathering in many a year.

There was an additional fillip to morale last night when they revealed another switcher from the Conservative party. Sam Gyimah, a talented minister in both the Cameron and May governments, was one of the 21 Tory MPs purged by Boris Johnson for rebelling against a no-deal Brexit. The increase in the contingent of Lib Dem MPs is the least important consequence of his switch. It is the signal that it sends to the electorate that really matters. The defection of liberal Tories such as Mr Gyimah and Sarah Wollaston sends a message to moderate Conservative voters that they ought to be making the same journey to the Lib Dems. The recruitment of Chuka Umunna and Luciana Berger says to moderate Labour voters appalled by what the party has become under Jeremy Corbyn that they too can have a new home with the Lib Dems.

Our latest Opinium poll puts the Lib Dems on a rating of 16 points; other recent polls have them at a similar level. This is not sensationally good. It is some way shy of their vote share in their best post-1945 general elections. But it is considerably better than flatlining on single figures, which is where they were less than a year ago.

Her party’s fortunes will be highly contingent on how she performs in an election campaign

Can they translate this promising context into success when the country goes to the polling stations? A lot will depend on Ms Swinson, who might be well known among dedicated Lib Dems, but is still introducing herself to the electorate. Not yet 40, she offers some obvious differentiation to the fiftysomething and seventysomething men who lead what we used to call the two main parties. One of her colleagues calls Ms Swinson “the wild card” of the looming election. A senior figure on Labour’s frontbench agrees, describing her as “the unknown quantity” among the party leaders. The voters are already well acquainted with Boris Johnson. In Jeremy Corbyn, Labour also has a highly polarising leader about whom opinions are fixed. Nigel Farage and Nicola Sturgeon don’t need any further introduction. Views of these personalities may flux a bit during an election campaign, but how they are perceived is not likely to be altered fundamentally. By contrast, Ms Swinson is still a blank page as far as most of the electorate is concerned.

Her party’s fortunes will be highly contingent on how she performs in an election campaign and no one can be sure about that until she is put to the test in that hot crucible of character. Tim Farron was thought to be a good campaigner when he became Lib Dem leader, but he sank their 2017 election effort when all the party’s messages were drowned out by questions about his attitudes towards gay marriage. Nick Clegg took everyone by surprise with the strength of his showing during the 2010 campaign. Hard though it is to believe now, there was a brief period when people talked about “Cleggmania” and one daft newspaper headline even suggested that he had become nearly as popular as Winston Churchill at the war leader’s zenith.

Ms Swinson secured the party leadership by a large margin in July, but there is a vast difference between pleasing Lib Dem activists and connecting with the wider country. The next election will not be just about Europe. Many voters will have other issues on their minds. We don’t know yet whether she has the skill to fashion an attractive pitch for her party that is broader than its opposition to Brexit. We will get some measure of whether she has what it takes from her conference speech.

We may also get a firmer idea about the extent of Lib Dem ambitions. Always outspent by Labour and the Tories at elections, they have a difficult choice to make about how high to aim. The cautious in their ranks argue that the party must be realistic about how many seats it can take off other parties and should concentrate its limited resources on their most plausible prospects. The bolder contend that they ought to risk spreading their resources more widely by pursuing an ambition to secure as many as 100 MPs.

They will need to prepare their defences against a big squeeze by the Tories and Labour. Both will try to turn the election into a binary choice between the two of them. Labour’s tortured transition towards being a pro-referendum party will not be very convincing so long as its leader still refuses to say whether or not Labour is now a Remain party, but Labour hopes to recoup some of the anti-Brexit voters who have migrated away from them to the Lib Dems. Ms Swinson is responding by trying to sharpen the difference with Labour. She will ask the conference to endorse a new policy, namely that a majority Lib Dem government would reverse Brexit by revoking article 50 without another referendum. This sounds fantastical, anti-democratic and a gamble. There will be fervent Remainers who feel exceedingly queasy about overturning the 2016 referendum without holding another one.

Both Labour and the Tories fear a strong Lib Dem performance, but it is the Conservatives who probably have most to lose in terms of MPs. Of the Lib Dems’ top 50 target seats, only seven are represented by Labour. The great majority of those target seats are Tory held.

One Conservative counter will be to attempt to turn the election into an extremely presidential contest, a Johnson versus Corbyn face-off, in the belief that this will best exploit the Tory leader’s superior leadership ratings. The Conservatives will tell the Corbyn-averse that a vote for the Lib Dems will risk putting him into Number 10. The Lib Dems have recent experience of how damaging this can be. David Cameron cannibalised a lot of their support at the 2015 election by shivering the spines of Tory/Lib Dem swing voters with the spectre that a vote for the Lib Dems could send Ed Miliband to Downing Street at the head of “a coalition of chaos”. That slogan has not aged well, given the mayhem that the Tories have inflicted on Britain in the years since, but fear of a repeat haunts the Lib Dems to this day. This explains why Ms Swinson is so adamantine about ruling out a post-election coalition with Labour for so long as it is led by Mr Corbyn, a man she calls “unfit to be prime minister”. It also explains why she was so brusquely dismissive over the summer when it was suggested that the Labour leader should be made a temporary prime minister to block a no-deal Brexit. The Lib Dems have many reasons for sending a clear message that they will not ease Mr Corbyn’s way into Downing Street. One of the most important is that it would set up the Tories to campaign on the slogan: “Vote Swinson, Get Corbyn.”

The latest defection to their ranks will embolden optimistic Lib Dems to think that we are on the cusp of a big realignment of our politics, the breaking of the blue-red duopoly that has controlled Britain for decades. The allegiance-smashing forces unleashed by Brexit certainly seem to have created the most promising outlook in decades. Ms Swinson likes to think so, saying that “the faultline in British politics is no longer a left-right divide... now [it] is between liberal and authoritarian values”.

I am old enough to recall Paddy Ashdown saying similar things back in the 1990s only for the big old beasts of blue and red to recover and reassert their dominance. The truth is we just don’t know yet. That question is far too large to be answered during a few days by the seaside. What we might get is some clues about whether the Lib Dems are really up to grasping their opportunities.

• Andrew Rawnsley is the Chief Political Commentator of the Observer