Nigel Farage has claimed there has been a "big" swing to the UK Independence Party in Eastleigh in recent days and the party is "coming up on the rails".
Many Lib Dems were "cheesed off" and turning to UKIP, its leader suggested.
Pointing to UKIP's strong performance in recent by-elections, he rejected claims the poll was a two-horse race between the Lib Dems and Conservatives, insisting it was "all to play for".
Campaigning is in its final days with voters going to the polls on Thursday.
The by-election was triggered by former Lib Dem cabinet minister Chris Huhne's resignation as an MP earlier this month after he pleaded guilty to perverting the course of justice over claims his former wife took speeding points for him.
'Coming up on the rails'
Huhne won the seat in 2010 with a majority of 3,864 over the Conservatives, with Labour in third and UKIP in fourth.
Mr Farage, who has spent several days campaigning in Eastleigh, said his party was fighting a "very hard" campaign this time around.
"The Eastleigh campaign is by far the biggest campaign UKIP has ever fought," he told BBC 5Live's Pienaar's Politics.
"We are a well-known party on the ground. We fight all the local election seats every year. We have got a good branch. In the last three or four days, what we have seen is a big growth in the UKIP vote but interestingly it has been coming predominantly from the Lib Dems."
The Lib Dems have said the Eastleigh contest is a straight fight between them and the Conservatives but Mr Farage said UKIP was "coming up strongly on the rails" with some polls suggesting support for his party was up 20% since the last election.
He suggested that in their "desperation" to retain the seat, the Lib Dems had been contacting some households as many as eight times and this was proving counter-productive.
UKIP recorded its best-ever performance in a by-election in November, when it got 21% of the vote in Rotherham. It also finished second in Middlesbrough and third in Croydon Central in other contests that month.
Mr Farage rejected suggestions that David Cameron's subsequent pledge of a referendum on EU membership after the next election had blunted UKIP's progress and insisted his party appealed not just to disgruntled Conservatives but supporters of all the three largest parties.
"The Westminster village have got the rise in the UKIP vote wrong," he added. "Where have we done well in by-elections - Middlesbrough, Barnsley. It is in the big hard Labour seats that UKIP has done well in the last 18 months."
The British public had "made the connection" between EU membership and "open-door immigration", he added. He said people increasingly believed that paying the EU "£50m a day" at a time when services were being cut at home was insupportable.
And UKIP MEP Gerard Batten said some polls suggested the party was now "neck and neck" with the Conservatives. It was a "myth" to suggest the party was just taking votes from the Tories as his party had "across the board" appeal.
"A lot of Lib Dem votes were protest votes anyway and that is what we are picking up," he told the BBC's Daily Politics.
The list of candidates in alphabetical order is:
- COLIN BEX - Wessex regionalists
- DAVID BISHOP - Elvis Loves Pets Party
- JIM DUGGAN - Peace Party
- RAY HALL - Beer, Baccy and Crumpet Party
- HOWLING LAUD HOPE - Monster Raving Loony William Hill Party
- MARIA HUTCHINGS - Conservative
- DIANE JAMES - UK Independence Party
- DR IAIN MACLENNAN - National Health Action Party
- KEVIN MILBURN - Christian Party "Proclaiming Christ's Lordship"
- JOHN O'FARRELL - Labour
- DARREN PROCTER - Trade Unionist and Socialist Coalition
- DANNY STUPPLE - Independent
- MIKE THORNTON - Liberal Democrats
- MICHAEL WALTERS - The English Democrats - "Putting England First!"