Sir Cyril yesterday predicted that Mr Ashdown would step down from the Liberal Democrat leadership if his party failed to make a breakthrough at the general election.
A former Liberal Democrat chief whip, Sir Cyril also warned Mr Ashdown against angling for a seat in a Labour Cabinet. "I don't think there would be any attempt to throw him out but I think he will resign," Mr Smith said on BBC radio.
"I have no quarrel with anything that Paddy has done except his unwillingness to sign the bottom line that he would not sit in a Labour Cabinet.
"If that possibility ever arose, then some of us would be taking action to stop it," he said.
With the Liberal Democrats struggling to stay in double figures in the opinion polls, Mr Smith's prediction of a bleak future for Mr Ashdown is being taken seriously at Westminster. Some Conservative ministers are betting that the Liberal Democrats will not increase their number of seats on 1 May.
It came as the Ashdowns looked certain to beat the Blairs and the Majors into Hello! magazine. The Liberal Democrat leader, who is soon to become a grandfather, has been invited to join the ranks of Fergie, Gazza and Madonna, who have all been in the glitzy publication.
An aide to Mr Ashdown confirmed that the magazine had approached his office, asking to do an "at home" piece with his 31-year-old expectant daughter Kate and her French husband Sebastian.
The proposed location of the Hello! spread has yet to be determined - whether it be the Ashdown's rose-clad cottage in the Somerset village of Norton sub Hamdon, or the small French village where Kate and Sebastian live.
"They have written to Kate, so it is up to her what she wants to do," said a party source.
Mr Ashdown, 56, is planning to visit his daughter in Burgundy in the last days of the election campaign in order to see her new baby, which is due in about three weeks.
The eldest of the three main party leaders, Mr Ashdown has since denied rumours that he is embarrassed by the idea of becoming a grandfather as it might conflict with his "Action Man" image.
The former Royal Marine has again been enjoying his outdoors profile on the campaign trail in the past week - driving a forklift truck and climbing on to a fire engine.
The party source said: "The baby is not going to be born until quite close to polling day. After that, Kate will have a think about it. They have written to her via the office, but it is her decision. All she's worried about at the moment is the baby."
He added that the Hello! spread was unlikely to appear before the general election.Reuse content