The voters in question live mainly in Eastham, a small, fractured district of the Wirral overlooking the Mersey, and one so far largely ignored in the frantic coverage of the constituency.
Known at the turn of the century as the Richmond of the Mersey for its attractive waterside landscape, Eastham has become the Lib Dems' sole strong- hold in Wirral South, and was largely responsible for the 6,581 votes the party managed at the last general election.
But this support could collapse come polling day, reckon their election rivals, because the Lib-Dems are seen as running a lacklustre campaign with a candidate from Liverpool who was only the party's third choice.
Eastham's electorate is now being eyed greedily by Labour, acutely aware that to overturn an 8,000-plus Conservative majority they need all the anti-Tory support they can muster.
The same point looms in Tory minds. "Eastham is likely to be crucial," says a local Conservative. "The question is, where are those Lib-Dem votes going to go?"
Ironically for a party which fears the Ashdown threat in a number of key seats, they are worried by what they see as a sluggish start to the Lib-Dem campaign. "They seem to have put up the white flag. We have seen very little of them," says Tory candidate, Les Byrom.
"I hope they do put up a proper campaign," he adds. "I do not like to see politicians just being forced down to their knees by circumstances." But such altruism scarcely masks the real Tory fear: that if the Lib-Dems voters desert the party it will be to Labour's likeable candidate, Ben Chapman.
The Lib-Dems have indeed not started well. Their preferred candidate was Phil Gilchrist, a popular and effective local councillor who is largely responsible for the party holding all three Wirral metropolitan borough council seats in Eastham.
When he declined to enter the race, pleading family reasons, they chose Neil Thomas, chief executive of a local training organisation, but he withdrew after a legal row with his employers.
Eventually it was up to Paddy Ashdown himself to pick up the phone and invite Flo Clucas, a prominent councillor across the Mersey, to take on the job.
"I was very flattered Paddy asked me," says Mrs Clucas, disguising any reluctance she may have felt at taking on the task.
She is clearly indignant at the "white flag" jibe, and at a Tory suggestion that she is fighting a single issue campaign on war pensions. "If anything, it's the Conservatives who have only one issue, with the way they are raising the issue of grammar schools," she says, in a reference to the endless attempts to put Labour on the spot over the future of two local selective schools.
Sitting in the makeshift campaign headquarters in Bromborough, Mrs Clucas, quick- tongued and good-naturedly combative, spells out what she sees as the main issues. "Health, the police and standards in education are the issues that people care about. The other two parties are just not addressing them."
She is also quick to reject the old claim that in a by-election so close to a national poll, a Lib-Dem vote is a wasted one. "If you want to change the Government and compel the Labour Party to spend more money on education, then the way to vote is for the Liberal Democrats."
So far she says she is encouraged by the doorstep response. "We were out on a bitterly cold night recently and were made to feel very welcome by everyone."
But Labour and Tories feel she could suffer from the "Liverpool factor" and lose supporters through her association with the city across the Mersey; an association underlined on Friday when Liverpool MP David Alton turned up to back her campaign.
Certainly Mrs Clucas, a French speaker with a passion for archaeology and education tutor at Liverpool Hope University, is far better known in that city, where she is deputy leader of the party's council group.
Labour activists have moved in fast, setting up a campaign outpost in the heart of Liberal Democrat territory, and the area is flooded with "Ben Chapman means business" posters. They know that despite media expectations of a spectacular win, the Wirral South is not a volatile seat but one with a solid Tory vote of almost 25,000 at each election, more than half the overall vote.
But Mr Chapman believes the message is getting across. "I have been told by people on the doorstep in Eastham who vote Liberal Democrat in local elections that they understand the only way to get rid of the Conservatives and bring about the changes they want is to vote New Labour in the by- election and general election," he says.
The Eastham ward has at least three distinct areas, making analysis of voting patterns difficult. Alongside the Mersey is the site of the old ferry dating from the 13th century. Pleasure gardens and a zoo were once popular Victorian attractions though much of this has now gone. But a semi-rural atmosphere is retained by the Eastham country park. Just inland is Eastham village, whose churchyard boasts a yew tree described as old in the 12th century.
But the main centre of population is the Mill Park estate, full of what the politicians describe as the "aspirant classes". Talking to locals there last week, it was clear that the Lib-Dems may be losing out to a new Labour swing. Ruth, a middle-aged shopper had always voted for councillor Gilchrist, "a good man who has done a lot for us," she said. "But I want a new government and I will probably vote for Labour. It's time for a change, isn't it?"Reuse content