The first telephone poll since Labour's manifesto launch, published exclusively in the Evening Standard, showed Mr Corbyn and the Labour Party gaining a modest boost.
"It will change our country", he said in his speech at the presentation of the manifesto in Bradford in northwest England.
Another, called Jim, suggested that she might face more of a challenge than expected in the June 8 general election after the launch of Labour's manifesto.
Labour said it will not try to overturn Britain's decision to leave the European Union, but will "negotiate a deal that preserves jobs and access to the single market" and maintains standards of workers' rights established under the EU.
The manifesto included a tax increase from 40% to 45% for salaries of between £80,000 (94,000 euros, $103,000) and £123,0000 a year, above which there will be a new 50% top rate of income tax.
Despite the rise in support for Labour, there are indications that Labour's support is "softer" than the Conservatives.
The party has insisted its plans are fully costed - raising taxes on big business and higher earners by £48 billion to pay for its programme to increase spending on education, health and other public services. However, Labour did not provide detailed costs for a plan to nationalise railways, the Royal Mail and parts of the energy industry.
His comments come amid reports that the Labour leadership will argue that Corbyn should remain leader if he can match the party's vote share of 30.4 percent at the last election under then-leader Ed Miliband.More news: Pressure still on Caps, but spotlight is on Fleury in Game 6
"This is a program of hope".
"The Labour Party campaign has outshone the Tories' comfortably".
In a telephone interview with POLITICO, the Unite leader pinned the blame for Labour's struggles on the media's "constant attack" on Corbyn, internal party divisions, and on public support for Prime Minister Theresa May "jumping on the bandwagon of hard Brexit".
"And I just say this too: this could be a young person's election because large numbers of young people are registering; for the first time those interested in politics want to have their say".
The Conservatives immediately slammed the plan as "nonsensical" and not properly costed.
And, in a comment that will infuriate many Labour activists and MPs, Mr McCluskey said: "I believe that if Labour can hold on to 200 seats or so it will be a successful campaign".
The IFS said: "The tax revenue that Labour's proposal would raise is highly uncertain".
"It's ordinary working people who will pay for the chaos of Corbyn", Treasury Chief Secretary David Gauke said in a statement.