Jim Murphy, a practising Catholic, is being urged to quit after his party lost all but one of its Scottish seats to the SNP.
Last week the Nationalists took 56 out of 59 possible seats.
SNP leader Nicola Sturgeon
celebrates election win
The day after the election, UK Labour leader, Ed Miliband quit his position but Mr Murphy said he wanted to remain in post.
But now he is facing calls to go, most recently from the leader of the Unite union.
Len McCluskey said Jim Murphy was responsible for "making certain" the Conservatives won the general election.
In an interview with the BBC's Newsnight, the union leader said Mr Murphy should "leave the scene".
He added: "There's no doubt in my mind that the late swing in the opinion polls was as a result of the anti-Scottish card that was played by Lynton Crosby and the Conservatives.
"They must have thought that all their Christmases had come early. And we have to examine that."
It is thought Mr Murphy, who once said "I'm pretty public about my faith; it's not a secret", will face a vote of no confidence in his leadership this weekend.
Elsewhere Left-wing Scottish Labour activists have urged him to go.
The Campaign For Socialism said it had reach an "almost unanimous decision that Jim Murphy must go".
Before the General Election the Catholic Church in Scotland appeared to criticise Mr Murphy.
In a letter to all 500 churches in Scotland bishops said that "on serious issues some politicians who profess a Catholic faith remain silent - or even surrender - in the face of grave ethical injustice."
Jim Murphy has been vocal about his Catholic faith in the past but has gone against Church teachings on several parliamentary votes.
In February 2013 the Labour candidate for East Renfrewshire voted in favour of gay marriage in England and Wales despite a campaign by the Church against the move.