Labour candidate Ian Murray has said his party has helped deliver "the worst Conservative prime minister in history".
Mr Murray, standing in Edinburgh South, stopped short of calling for Corbyn to stand down saying the party should "wait and see" the full election results before deciding whether there should be a new leader.
A Labour source told the PA news agency the party is likely to hold the seat, but predict Mr Murray's majority will fall from 15,514 in 2017 to around 6,000.
Mr Murray said: "I feel sorry for constituents up and down the country, in all four corners of the country, that need a Labour government - they've been badly let down by the Labour Party.
"We've delivered a hard-right Conservative government with the worst Conservative prime minister in history, and I think we should all reflect on that."
Mr Murray was the only Labour MP in Scotland following the 2015 election.
He said voters he spoke to on the doorsteps during this campaign did not see Mr Corbyn as prime minister and could not see Labour as a credible alternative government.
He told the BBC: "This Labour Party is now at its last chance in the last chance saloon.
"I merely plead to Labour Party members tonight - we either want to be in government and throw this Conservative Party out and transform the country, like the Labour Party has done before, or we allow a Conservative majority tomorrow morning, and wake up as Labour Party members being incredibly sad about that.
"Not just because of what that means, but because we have let every single person in this country who is desperate for a Labour government down."
