MP Sarah Wollaston said she would consider leaving the party if Mr Johnson became leader.
"I think he says things as a public political figure which a lot of people are thinking, that most people dare not tread".
Writing in the Mail on Sunday, Mr Johnson lashed out at the Northern Ireland 'backstop, ' aimed at making sure there is no hard border with Ireland.
Former Army officer and member of the Foreign Affairs Select Committee Tom Tugendhat said Johnson's comments were not the sort of thing to joke about - Tugendhat had seen the horrors caused by suicide bombing first hand, after an attack happened outside his office in Helmand province, Afghanistan.
Alastair Burt said there can be "no justification for such an outrageous, inappropriate and hurtful analogy" and urged politician to stop "this extraordinary use of language" over Brexit.
Number 10 said the Chequers proposal, which was agreed in July and led to the resignations of Boris Johnson and then Brexit Secretary David Davis, was "the only plan on the table", despite threats that up to 80 Tory MPs could vote against it. "We look like a seven-stone weakling being comically bent out of shape by a 500lb gorilla", he wrote.
Home Secretary Sajid Javid - viewed as a potential leadership rival - rebuked his former Cabinet colleague, saying: "I think there are much better ways to articulate your differences".
"The Brexit Minister must assume the role of the Government's political bomb disposal officer protecting the United Kingdom from the efforts of the bullies in Brussels to blow apart the Union or blast the result of the peoples' choice in the referendum to break the bands of EU bondage".
Backbench Tory MP Nadine Dorries said Johnson's critics were "terrified of his popular appeal".
When negotiating, the prime minister needs to demonstrate her intent and also her power to deliver, Mr Baker told the Press Association.
He added: 'We have opened ourselves to perpetual political blackmail. Grieve said Johnson's phrasing in the Mail on Sunday article was "entirely in character: crude but, for some, entertaining populist polemic."He said there was a lack of coherent thought in the article".
On Friday, Mr Johnson and his wife Marina Wheeler, both 54, announced they have separated and are going through the process of divorce. In 2004, he was sacked as Conservative vice chairman after lying about an extramarital affair.
Johnson's comments came as the Sunday Times revealed that May's aides have assembled a secret dossier with "lurid allegations" about Boris Johnson's sex life in an apparent effort to prevent him from becoming prime minister.
Downing Street and Conservative Campaign Headquarters (CCHQ) categorically denied circulating the document or ordering any updating of the dossier.
According to the paper, the document warned that concerns around medical supplies could "feed civil disorder", and that potential goods shortages raised concerns of "widespread protest which could then escalate into disorder".