While signs out of Scotland were that the SNP was poised to take every seat but one, the part advised the exit poll result be treated with caution.
Ms Sturgeon tweeted: "I'd treat the exit poll with HUGE caution. I'm hoping for a good night but I think 58 seats is unlikely!"
Former Labour spin doctor Alastair Campbell was in a state of disbelief over the predictions.
"I hope that these figures are wrong. I hope the exit poll is wrong. I won't eat my hat, but I will eat my kilt if they (the SNP) get 58 seats," he said.
Derek Mackay, transport minister and SNP business convenor, told the BBC: "Talk about managing expectations... I think the SNP is probably going to have quite a good night. But 58 feels somewhat high on the optimistic side."
Mr Mackay told the BBC an anti-Tory majority could still be possible if the exit poll is borne out.
He suggested former Labour voters who voted yes in the independence referendum last year may have come over to the SNP.
Asked if Labour leader Ed Miliband would consider a deal with the SNP, Ms Dugdale said the message was the same before and after 10pm.
She told the broadcaster: "The message is very clear. It's the same before 10 o'clock as it will be after... There will be no deals with the SNP."
She said it was up to the SNP to keep its promise not to support the Tories.
But Mr Mackay replied: "I'm sure the Labour party has the brains to propose a Queen's Speech and Budget that the SNP will support."
Meanwhile, Labour deputy leader Harriet Harman urged caution over the national poll, telling the BBC: "I have been on television where I have been commenting on exit polls in the past where the exit polls were wrong, because it is difficult to read these situations from exit polls."
Asked if Mr Miliband could continue as leader if the poll proved correct, she said: "Well, at this stage we are just waiting for the counts and seeing whether or not David Cameron has got a House of Commons voted in which is prepared to give him a majority.
"You will forgive me for actually waiting until we have the answer to that big question before we go on to any other hypotheticals."
Alastair Campbell said: "Looking at the results, David Cameron set out to win a majority, it looks like he hasn't.
"I don't know what he is going to do in relation to the Liberal Democrats.
"If the polls are wrong, if David Cameron cannot form a government which can command the confidence of the House of Commons, then Ed Miliband even on those numbers be asked to form a government."
Elsewhere, a rival of Boris Johnson said he had "no moral compass" and his potential return to the Commons would be a "really bad day" for the constituency he is hoping to represent.
Michael Francis Cox, the Liberal Democrat candidate for Uxbridge and South Ruislip, said the campaign had been "pretty grim" because the London mayor had taken "little interest" in the west London constituency.
Mr Johnson is hoping to return to the Commons by winning the safe Tory seat after spending nine years as MP for Henley until 2008.
Former deputy chief whip Sir John Randall, who has stepped down, won the seat for the Conservatives in 2010 with a 11,216 majority.
Votes were last night being counted at Brunel University in Uxbridge where ballot boxes arrived shortly after 10pm.
Speaking at the university, Mr Cox, who was the first candidate to arrive, said Mr Johnson had been an "elusive main candidate" who had spent little time in the area "other than the odd photo opportunity".