"Top-level cabinet resignations usually spell trouble for a government and Boris Johnson's might well have led to a leadership challenge, but May appears to have emerged unscathed from a meeting of her party, for now", said Al Jazeera's Jonah Hill, reporting from London.
Hunt, the MP for South West Surrey, has served as Health Secretary since 2012. "If the government plans to get the deal through on the back of Labour Party votes, that would be the most divisive thing it could do, and it would be a split coming from the top".
"Brexit should be about opportunity and hope", Johnson said in a scathing resignation letter that was echoed in headlines in a number of Britain's national newspapers. Under Conservative Party rules, a leadership race could be triggered if at least 48 of her MPs declared their support for one. He said "the Brexit dream is dying, suffocated by needless self doubt".
Johnson's departure came a day after David Davis, the British minister in charge of Brexit negotiations, also stepped down in protest of May's new Brexit strategy that pointed to a more "business-friendly" deal with the EU.
"My concern is about the policy rather than the individual", he said.
Another said the second resignation made the looming October deadline highly unlikely as Mrs May attempts to rebuild her Cabinet.
"I heard last night it might be delayed so I think it bodes well that we can sit down to hammer out a deal which is good for the United Kingdom and the EU".
With Britain due to leave the 28-nation bloc on March 29, 2019, European Union officials have warned Britain repeatedly that time is running out to seal a deal spelling out the terms of the divorce and a post-split relationship.
The man leading the UK's negotiating team, David Davis, resigned late on Sunday night, saying that he did not agree with the UK's proposals, so was the wrong person to be going into negotiations with them. They also argued that the proposals breach several of the "red lines" that the government had set out, including a commitment to leave the EU's tariff-free customs union.
After Mr Davis' resignation, European Union diplomats laughed off any possible effects on the Brexit negotiations, insisting the Prime Minister's European Union sherpa Olly Robbins is the UK's main man in Brussels these days.
Dominic Raab, a Brexit supporter and former housing minister, was appointed to replace Davis only days before negotiations in Brussels are due to resume next week.