Anna Soubry, one of the leading rebels, initially hit out at the "blatant bullying" by the newspaper of those who intend to defy the government.
Tory rebels have indicated they will vote against the government's plan to enshrine the UK's exit date in law, which could cause the amendment to be defeated.
"If fighting for the best possible future for our country and our government is considered mutiny - then bring it on", tweeted one MP, Heidi Allen.
She told MPs: "None of the people who have been named - I take it as a badge of honour - want to delay or thwart Brexit".More news: Britain's Johnson to meet husband of aid worker jailed in Iran
"We just want a good Brexit that works for everybody in our country", she said.
Even ardent Brexiteers quickly sought distance from the paper's coverage with Brexit minister Steve Baker stating that "I regret any media attempts to divide our party" and Dominic Raab signalling his agreement.
"My Parliamentary colleagues have honest suggestions to improve the Bill which we are working through and I respect them for that", Mr Baker said.
But despite the revolt, the measure passed through Parliament easily during the first day of debate over whether to amend the EU Withdrawal Bill.
They argue that the move will limit the Prime Minister's flexibility if negotiations with Brussels drag on until the last minute.More news: Officials responding to reported shooting near elementary school in Rancho Tehama
Britain trigged the two-year Article 50 process of leaving the European Union on March 29 this year, but this can be extended if all 28 European Union member states including Britain agree.
Last week the prime minister vowed that the United Kingdom would leave the EU at 11pm on March 29, 2019, and tabled an amendment to her European Union (Withdrawal) Bill.
They were joined by most Lib Dem and SNP MSPs - but were heavily outweighed by more than 300 Tory and DUP figures who voted in support.
"We're going to leave. I didn't. My goal is to try to make sure that Brexit is as controlled and risk-free a process as possible".More news: Weather Agency: Magnitude 5.4 Earthquake Hits North Gyeongsang Province
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