Jo Swinson could to lose her seat for Dunbartonshire East to the Scottish National Party (SNP), according to exit polls.
But the joint-leader of East Dunbartonshire council has said "it is on a knife edge".
Andrew Polson, a Conservative councillor, said: "My gut reaction is that she might scrape through, but it's on a knife edge."
According to Mr Polson's figures, Jo Swinson is polling 44 per cent in his Bearsden South ward, which he described "strong Tory" area.
He said: "You would really expect her to be polling 50 per cent.
"She's holding up in Bearsden, but the SNP have increased their vote. They're polling 23 per cent there, when you'd be expecting around 15 per cent, so it's on a knife edge."
He said his sense from Conservative supporters in his ward was that they were voting for the Tories rather than voting tactically to keep out the SNP.
"We were definitely getting on the doors in our ward: 'We're sticking with you this time - the last two elections we voted Jo but we're sticking with you this time'," he added.
Mr Polson also suggested there was a significant number of remain-voting constituents who thought the Liberal Democrat's policy of revoking Article 50 was a "threat to democracy".
