Reports suggested the Prime Minister would face a vote of no confidence in her leadership.
Labour MP Andrew Adonis said Raab's appointment could spell the "death" of the Tory leader, while writer and editor Hitcham Yezza said Brexit has now become even more "shambolic".
Less than nine months remain until Britain reduces the EU's membership on March 29, 2019.
Just 30% of Britons think Theresa May is the best Conservative to lead Brexit negotiations, with 44% saying someone else within the party would be better suited, and 26% answered that they don't know.
Now, Downing Street believes that the hot water the prime minister is in today will shock European Union leaders into realising they need to start compromising themselves - not just perpetually demanding capitulations on the UK's red lines.
Mr Johnson wrote: "Brexit should be about opportunity and hope".
That makes negotiating a deal with the European Union very hard: The bloc has said that Britain can't pick and choose the "four freedoms" (free movement of goods, capital, services, and people) and have an "a la carte" Brexit.
While some Labour lawmakers might be tempted to vote for a Brexit that kept the United Kingdom inside the EU's customs union, they too were clear that the prime minister's proposals didn't go almost far enough.
May said that Britain would not look to extend Article 50, the notice of intention to leave the European Union, and that British people wanted the government to deliver Brexit rather than voting again on the deal.
On Tuesday morning Theresa May held her first cabinet meeting after the reshuffle.
The outgoing Brexit secretary said the government had gone further than it should have in the negotiations, in a "dangerous strategy".
"May is fighting for her survival", Mujtaba Rahman, a managing director at Eurasia Group, said in a research note.
Under Conservative Party rules, a confidence vote in a leader can be triggered if 48 lawmakers from May's Conservative Party request one.
The British leader may have stilled the waters over a possible leadership contest, but some Conservative Brexit supporters are still incensed over what they see as her decision to break her promise for a clean break with the EU.
But others argued May had adopted the most realistic plan after she was weakened in an ill-judged election past year when she lost her parliamentary majority, meaning she has to rely on a small Northern Irish party to govern.