The comments, from SNP MP Drew Hendry, come as former Scottish Tory MSP said it would not be possible for Mr Ross to lead the Scottish Conservatives at another general election if the Prime Minister is still in post.
Last week, Mr Ross called on Mr Johnson to resign after the Prime Minister admitted attending a “bring your own booze” event in Downing Street on May 20, 2020.
All 31 of the Scottish Conservatives’ MSPs have backed Mr Ross, but questions have been asked about both the future of the leader and the association of the party with its UK counterpart should Mr Johnson stay in post.
The SNP have repeatedly called for Mr Johnson to resign and on Sunday said it would be “absurd” for Mr Ross to fight another general election campaign with Mr Johnson as party leader.
Mr Hendry, the MP for Inverness, Nairn, Badenoch and Strathspey said one of the two Conservative leaders must resign or step down.
"The situation is ludicrous and completely unsustainable. It would be absurd for Mr Ross to fight a general election, or an independence referendum, beneath a Prime Minister he has openly admitted is unfit for office and should resign.
"And, with senior Tory Cabinet ministers dismissing Mr Ross as a 'lightweight' nobody, whose views they simply brush aside and ignore, how can anyone in Scotland take anything they say seriously?
"If Boris Johnson doesn't resign there will inevitably be questions over Mr Ross's own position and how he could possibly limp on without any credibility.”
Civil servant Sue Gray has been set the task of establishing the facts around the gatherings held in Downing Street, with many Tory MPs waiting for the results of her report before committing to a potential leadership election.
A spokesman for the Scottish Conservatives said: "Last year the Scottish Conservative and Unionist Party won 100,000 more votes than ever before under Douglas' leadership.
"He will not be resigning, no matter how eager the SNP are to get ride of him."