Launching her manifesto, Mrs Beckett said changing the debate was a challenge facing Labour 'even within the ranks of our own party'.
After clashing with Mr Blair last week over her call to sweep away Tory trade union legislation, Mrs Beckett said unless Labour succeeded in breaking out of Tory thinking, 'we will allow the Tories to fetter political debate. We will allow them to put a cap on our aspirations . . .
'We need to alter the political climate and set people free to have their heads in the clouds, even while their feet stay firmly on the floor.'
Clare Short, her campaign manager, said: 'We are not into knocking copy, but we think Margaret is the strongest unifier among the candidates.'
Mrs Beckett refused to commit herself to serving in a Blair Shadow Cabinet if she failed to win either the leadership or deputy leadership. Dawn Primarolo, a member of her campaign team, said: 'She is going to win.'
Mrs Beckett's press conference was attended by leading members of the Campaign Group of left-wing Labour MPs, including Ken Livingstone, Harry Barnes, Bernie Grant, and Ms Primarolo, a party health spokeswoman.
Mrs Beckett's team said her campaign was being received 'warmly' in trade unions and constituencies, which make up two-thirds of the electoral college, which will choose the leader in ballots for 21 July. But it is thought the real battle is now with John Prescott for the deputy leadership. They are both appealing to the left and centre of the party.
She made it clear that on two key parts of the welfare state, she is not willing to change. Mrs Beckett reaffirmed Labour's commitment to the universal uprating of child benefit and state pensions.
Some modernisers in the party, who support Mr Blair for the leadership, believe Labour's 1992 election commitment to uprate pensions and child benefit for rich and poor alike should be replaced with a commitment to redirect the savings in more generous benefits to the needy. The Tories are studying such plans for targeting in the review of social security planning.
Any attempt to change the commitment would be highly controversial and Labour leaders have refused to make commitments until after the party's Social Justice Commission has reported on its recommendations for reforming the welfare state. Underlining her resistance to any change, Mrs Beckett said: 'Universal child benefit and the universal state pension are both desirable and necessary.'
She hoped Labour would update the framework within which these benefits were paid. The glossy campaign leaflet underlined the strength of her leadership qualities and experience, with a photograph of Mrs Beckett with Bill Clinton, the US President.
Mrs Beckett's campaign leaflet presents her as the natural successor to John Smith as a unifier of the party. 'A good leader is someone who gives people space, someone who gives people confidence and support, someone who has the ability to draw on all the talents across our broad church,' she says. 'I have accepted nomination to lead our party to continue the inclusive style of leadership established by John Smith.'