MEP Patrick O'Flynn said the party's support had broadened in the final days of the campaign and suggested their vote share would be more than 10%.
Earlier, deputy chairman Paul Nuttall said UKIP MPs could offer vote-by-vote support to a minority government.
But he told the BBC a referendum on the UK staying in the EU was a "red line".
UKIP is attracting around 14% support, according to the latest BBC poll of polls.
The party had two MPs at the end of the last Parliament - both of whom won by-elections after defecting from the Conservatives.
The party's leader, Euro-MP Nigel Farage, is standing for election to the House of Commons in the Kent constituency of Thanet South. Here is a full list of the candidates contesting the seat.
Speaking about UKIP's prospects, economy spokesman Mr O'Flynn said the party had managed to defy expectations of a squeeze.
He said: "Tomorrow we will significantly and perhaps dramatically outperform the expectations of pollsters and pundits alike.
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"That means doing much better than a political class consensus of a vote share of around 10% and one or two seats in the Commons.
"The so-called squeeze on the UKIP vote predicted by so many of the media class simply has not happened.
"On the contrary we are getting indications of a very substantial energising and broadening of our support in the final days of the campaign."
Speaking on BBC Radio 4's Today programme, Mr Nuttall repeated that his party would not enter a formal deal after the election.
He said: "We've made it perfectly clear there will no coalitions, there will be no pacts, and if we did go down the line of a deal whereby we vote with the government on a vote-by-vote basis, it will be a loose deal."
He said a "red line" would be a "free, full, fair referendum" on EU membership "as soon as possible, preferably before the end of the year."
Mr Nuttall was asked whether a vote for his party could harm the prospects of Tory success and therefore an vote on the EU.
He said: "The problem you've got with Mr Cameron's promise of a referendum is one he's promised a referendum before and gone back on that deal and secondly he's talking about a negotiation through 2016 and into 2017 with an organisation that has made it perfectly clear that renegotiation isn't on the table."
He added: "We're looking to get as many votes as possible tomorrow to ensure we have real change in British politics, whether that's with the European Union or indeed electoral reform."
The best of BBC News' Election 2015 specials

English Heritage has organised the trek on horseback and foot from York to East Sussex to mark the 950th anniversary of the famous clash.
The volunteers will arrive on the battlefield 950 years to the day since Harold fought William of Normandy.
Nigel Amos, leader of the march for English Heritage, said it was a "once-in-a-lifetime opportunity".
King Harold defeated a Viking army at the Battle of Stamford Bridge in East Yorkshire, on 25 September, 1066, before travelling south to face the Normans.
On 14 October, he fought and was killed at the Battle of Hastings.
William then seized the English throne.
Emily Sewell, head of events for English Heritage, said 1066 and the Battle of Hastings was "one of the most famous battles and most transformative years in English history".
Nigel Amos, who is leading the march on behalf of English Heritage, added: "There's nothing like a personal experience to understand what it was like and offer an even more authentic window on that world to inspire and inform others."
The UK Independence Party (UKIP) will "significantly and perhaps dramatically outperform" expectations in Thursday's election, a spokesman has predicted.
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A group of "warriors" are staging a 300-mile march to echo King Harold's journey to the Battle of Hastings.