Meanwhile, No 10 is said to be alarmed at the prospect of MPs taking control of Brexit if Tuesday's vote is lost.
The Observer newspaper reported Sunday that its lawmakers have been told it could be tabled "within hours" of that on Tuesday, with the confidence vote to be held the following day.
Lawmakers who believe it either leaves Britain too close or too distant from the bloc, fired ominous warning shots this week, voting to force the prime minister to quickly set out an alternative plan for Brexit if she loses the vote.
"And there is a problem that if you have a referendum and you tell everybody that you're going to observe the result and do what the people decide, the referendum was not about trade agreements, it was about whether as a country we want to take our own decisions in the world".
Corbyn confirmed that he would not consider supporting the government in the meaningful vote on Tuesday, despite Theresa May's last-ditch attempts to garner support for her deal from members on the opposition benches.
At least two groups of rebel MPs are plotting to change Commons rules so motions proposed by backbenchers take precedence over government business, upending the centuries-old relationship between executive and legislature.
Described as "a very British coup", the plan would see May lose control of parliamentary business to MPs, threatening her ability to govern, the newspaper said.
Mr Hunt warned that failure to deliver Brexit would be "incredibly damaging" for the United Kingdom and something the country would regret for "many, many generations".
May's deal has come under fire from all sides - with opponents of the European Union seeking a cleaner break and many pro-Europeans pressing for a second referendum.
Meanwhile, Work and Pensions Secretary Amber Rudd said she is "committed" to ensuring that the United Kingdom does not leave without a deal.
May has urged Parliament to support her little-loved European Union divorce deal so that Britain doesn't leave the European Union on March 29 without an agreement on exit terms.
In a significant shift of tone apparently created to win over hardline Brexiteers who have set their faces against Mrs May's deal, Mr Hunt warned that defeat next week would not necessarily provide MPs with the opportunity to choose their preferred version of Brexit.