Mr McCluskey's intervention came hours after Mr Corbyn launched his party's manifesto, which the Labour leader described as a "programme of hope" and which included billions for schools and the NHS and an expansion of free childcare.
Mr McDonnell, a key ally of the Labour leader, said he did not accept anonymous sources any more after a BBC journalist said he had spoken to Labour candidates who did not want help from Mr Corbyn.
A survey conducted by Trinity Mirror newspapers including the Birmingham Mail and Birmingham Post found support for the Labour Party had actually risen slightly in the West Midlands region.
But they do give an indication as to whether the support for each party is increasing or falling.
Mrs May said that the Tory manifesto later this week will "set out in detail the five great challenges our country faces over the next few years and lay out how we will tackle them", compared to the "fantasy wish list of easy promises paid for with imaginary money" offered by Labour.
Guided by the strapline "For The Many: Not The Few", Corbyn's manifesto seeks to impose £50 billion in annual tax rises for top United Kingdom earners (+ £80,000 per year), combined with a return to nationalising United Kingdom civic services such as the Royal Mail, National Grid and transport sectors.
Brexit is also mentioned in the manifesto with Labour pledging to refuse to leave the European Union with no deal in place.
We have seen yet again from Jeremy Corbyn's Labour Party today that a Labour government led by Jeremy Corbyn would not be unequivocally committed to the Trident nuclear deterrent.
Mr Corbyn's allies believe he is likely to be able to stay in office should he win more than the 30.4 per cent share of the vote which Ed Miliband achieved in the 2015 election.
And in the 2010 general election, led by Gordon Brown, Labour got 29 per cent of the vote. I feel full of confidence now that the opinion polls can start to change. But as Labour's senior figures say - and senior Conservatives too - the only way we'll know for sure is when the real votes are counted.
The 35% support for Labour recorded by YouGov for the Sunday Times is the best rating for the party since March previous year before the divisive European Union referendum and the abortive challenge to Mr Corbyn's leadership.
It does seem that Theresa May's Conservative Party has been more successful at convincing voters that they are now the real part of Brexit.