Three Labour leadership contenders have 48 hours to get enough support from MPs to be able to stand in the contest.
Andy Burnham, John McDonnell and Diane Abbott are currently short of the 33 nominations needed to get onto the ballot paper for the election.
The three have pushed their case at a meeting of the GMB union in Southport.
But Mr McDonnell came under fire for saying the best way to have improved life in the 1980s would have been "to assasinate" Margaret Thatcher.
The remark was immediately condemned by Conservative commentators.
The three men seen as the frontrunners in the contest - former Cabinet ministers David Miliband, Ed Miliband and Ed Balls - have already got the necessary votes.
But the remaining contenders have yet to clear the hurdle.
Former Health Secretary Andy Burnham has 23 nominations while backbench MPs John McDonnell and Diane Abbott have ten and 8 nominations respectively.
With two days left before nominations close, more than 70 Labour MPs have yet to declare their support for any of the candidates.
Five of the contenders took part in a hustings at the GMB annual congress on Monday, with Mr Balls unable to attend because of commitments in Parliament.
Mr Burnham said the Labour movement was still in "good heart" despite its election defeat and argued his background and experience in politics made him the man to win back voters the party had lost in recent elections.
He said he would provide a "real contrast" with senior figures within the coalition government and criticised what he said was the "elitist", "top-down" way the former Labour government had dealt with grass-roots opinion within the party.
'Organise not mourn'
Mr McDonnell said the party needed to "organise not mourn" after its defeat and pledged to return public sector jobs transferred to the private sector under successive government back into public hands.
"It is a disgrace that New Labour privatised more jobs than Thatcher and Major put together," he said.
Mr McDonnell, who is on the left of the party, went on to say that he had been asked recently what single act he believed would have most improved life in Britain in the 1980s.
"I said, look, I was on the GLC that Mrs Thatcher abolished. I worked for the National Union of Mineworkers (NUM) and we had the NUM strike. I think I'd assassinate Thatcher."
The BBC's Political Correspondent Ross Hawkins said the comment - which was met with enthusiastic applause by union activisits - should be seen in the context of the audience it was directed at and the fact Mr McDonnell and the other MPs were explicitly appealing for votes.
Describing the contest as a "turn the page election" for Labour, Ms Abbott also pledged to fight spending cuts, claiming the coalition government wanted "to reconstruct out of existence" public services that people relied upon.
David Miliband, who currently has 63 nominations, told union members that Labour had a "massive task" ahead of it and the party had to "catch up" on issues such as housing and anti-social behaviour.
Ed Miliband, who has 49 nominations, said Labour needed to listen to the trade unions more and develop a strong programme for government while in opposition.
The next Labour leader will be chosen by a ballot of MPs, MEPs, party members and members of affiliate organisations including trade unions. The result will be announced on the first day of the party conference in September.