"I think if the prime minister makes further concessions with the European Union then there will no doubt be more resignations from Brexiteers in the Cabinet, from junior ministers to PPSs, because there is only so much that you can give in a negotiation", she told BBC2's Newsnight.
The four amendments to the crucial Customs Bill were put down a day before Thursday's publication of a White Paper setting out the British prime minister's plans, which infuriated Leavers and prompted the resignation of Cabinet ministers Boris Johnson and David Davis.
And former Conservative leader William Hague warned party rebels that voting against the Prime Minister's final deal could result in Brexit being indefinitely delayed or halted altogether.
Hunt, who served as the health secretary, was assigned to his new role late on Monday hours after Johnson handed in his resignation letter to May.
May, who has tried to keep calm and carry on, said in a tweet that it was a "productive Cabinet meeting" and that she was "looking forward to a busy week". "Maybe I'll speak to him when I get over there".
They will demand the government scrap its offer to collect tariffs on behalf of the European Union when the Customs Bill returns for debate - a crucial element of the prime minister's plan for a "facilitated customs arrangement".
That was despite the likes of Mr Johnson and Mr Davis privately expressing their reservations about the prime minister's strategy.
"There is no stronger alliance than that of our special relationship with the United States and there will be no alliance more important in the years ahead", the British leader said.
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Solicitor General Robert Buckland said: "She talked about Corbyn, she talked about the alternative which is delivering the country to the sort of government that I don't think people have voted for and certainly any Conservative voter would be repelled by".
"We're two years on from the referendum and the party of government seems more divided than ever", the Labour MP said.
Other pro-Brexit Cabinet ministers said they supported May and would not resign.
The foreign and Brexit secretaries have both quit over the plans. This policy will be bad for our country and bad for the party.
The UK has spoken of boosting the Commonwealth and forging a free trade pact with India after Brexit, but that will not be easy if Britain refuses to budge from its tough position on movement of people and visas.
The pair said they have stood down as they oppose Theresa May's Chequers policy on Brexit.
"We deliver that Brexit and we do it in a way that protects jobs and livelihoods and meets our commitment to Northern Ireland", she said.
And in an article for The Scotsman today, Ms Sturgeon writes: "After the Davis and Johnson resignations, it is highly questionable whether there is a majority for the Chequers plan as it stands".