Jo Swinson has accused Boris Johnson of showing “an empathy bypass” in his attitude to other people, as the Liberal Democrats made a final push to persuade traditional Labour supporters to vote tactically and deny the Conservatives a majority.

Speaking to the Guardian during a campaign rally in Bath, Swinson said her party could confound gradually falling national poll ratings to spring a series of surprises in up to a dozen or so Conservative-held seats, if the anti-Tory vote coalesces.

The Lib Dem leader said the task of denying Johnson a majority was all the more urgent following his much-criticised ITV interview in which the prime minister repeatedly refused to look at a photograph of Jack Williment-Barr, the four-year-old boy pictured sleeping on the floor of an overstretched A&E unit in Leeds.

Calling Johnson’s approach astonishing, Swinson said it fitted a wider pattern of behaviour, such as over the case of Nazanin Zaghari-Ratcliffe, the British-Iranian woman jailed in Iran, and his dismissal as “humbug” female MPs’ concerns over inflammatory political language.

“It’s tone deaf. It’s like he doesn’t respond to people as human beings,” Swinson said. “It’s like he has had an empathy bypass. Does he care about anyone? I can only conclude that he just doesn’t really care. It’s a pretty damning conclusion, but that’s the situation.”

Such a person, Swinson said, “doesn’t deserve to be prime minister”.

“He’s a danger to the future of this country. That’s why he’s prepared to say anything he thinks will work on Brexit, regardless of whether he can do it, regardless of what the consequences will be.”

Lib Dem rhetoric at the start of the campaign, which talked up Swinson as a prospective prime minister, has been notably less evident as the party’s poll rating fell from 20% to about 13%, with the focus now very firmly on stopping Johnson.

An internal Lib Dem analysis document of a series of Conservative-held seats, which combines polling with local canvassing, claims that as well as much-touted London constituencies such as Finchley and Golders Green, the party is running close in a number of remain-minded commuter belt areas.

The document says that if enough Labour waverers can be persuaded, upsets could occur in not only Dominic Raab’s seat of Esher and Walton, but also Hitchin and Harpenden, held by Tory Bim Afolami, and Wokingham, where John Redwood had a near-19,000 majority in 2017, among others.

It argues that with two-thirds of Labour voters identified during canvassing as saying they could vote tactically, victories in 10 such surprise seats, as well as in some more traditional Lib Dem-Tory marginals, could be “what stands between the Tories and an overall majority”.

Such projections will be dismissed with scorn by opposition parties, and treated with scepticism by psephologists, but the analysis highlights the Lib Dems’ best-case path to exceed expectations in what has so far been a somewhat disappointing campaign.

Swinson said the last couple of days of the election were set to be “absolutely crucial”. She said:”There’s a lot of people who only really tune into the election at this time, they haven’t followed the twists and turns, or watched every debate, and they’re now making a decision. So it’s often at the last minute you get this tactical swing.”

Swinson herself has endured a fairly gruelling campaign, including mixed personal poll ratings and some bruising public feedback on several Lib Dem tactics, notably the policy to cancel Brexit without a referendum if her party won an absolute majority in the Commons.

Asked if she regretted the move to push the policy through the Lib Dems’ conference, despite some scepticism from delegates, Swinson said: “Obviously, we’ll reflect on this campaign afterwards, and do all of that. But at the end of the day it’s fundamentally honest.

“We started the campaign at a time when, in the summer, we’d seen four parties all hovering around 20%, and in a first-past-the-post electoral system that opens up the potential for quite seismic shifts. I’m just not going to apologise for being ambitious in an election where so much is at stake.

“The corollary of that is, in what scenario would a Liberal Democrat government negotiate Brexit? It’s hard to imagine. So I think we had to be upfront with people.”