But critics warn the European Union withdrawal bill - also known as the repeal bill - represents a power-grab by ministers, while others see the legislation as a chance to shape the prime minister's Brexit policy.
The targets of the piece accused the paper of "bullying", while a government minister distanced himself from what he said was an attempt to "divide" the party.
Heidi Allen, a Tory MP also pictured on the newspaper's front page, tweeted: "If fighting for the best possible future for our country and our government is considered mutiny - then bring it on".
Pro-EU ex-minister Anna Soubry, described it as a "blatant piece of bullying that goes to the very heart of democracy". We want a good Brexit not a hard ideologically driven Brexit.
"The role of MPs is not to be lobby fodder but to scrutinise legislation", tweeted Antoinette Sandbach, referring to the lobby areas in which lawmakers vote.
Veteran MP Clarke labelled the amendment to make the day the United Kingdom leaves the European Union binding, making sure that Brexit happens at 11pm on 29 March 2019 "utterly foolish" and "silly".
Among the critics of the Daily Telegraph's "mutineers" headline was Brexit Minister Steve Baker, who tweeted: "I regret any media attempts to divide our party".
He tweeted: "Parliamentary colleagues have honest suggestions to improve the Bill which we are working through and I respect them for that".
MPs, including from the Conservative party, have tabled 188 pages of amendments to the bill, which will be debated in groups over eight days spread over the coming weeks.
Former Cabinet Office minister Sir Oliver Letwin told MPs that he would vote with the government on Tuesday night, but the part of the withdrawal bill that deals with retained European Union law is a "frightful mess".
They argue that the move will limit the Prime Minister's flexibility if negotiations with Brussels drag on until the last minute.
"Named and shamed" MPs include Nicky Morgan, the former education secretary who now chairs the Treasury Select Committee; Sarah Wollaston, who chairs the Health Select Committee; Dominic Grieve, the former attorney-general; and former Chancellor Ken Clarke. "I didn't. My goal is to try to make sure that Brexit is as controlled and risk-free a process as possible".