In an interview with BBC Radio 4's Today programme, 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".
On Friday, her foreign minister Jeremy Hunt said Brexit might not happen at all if May's deal was defeated. You have delivered your instructions. As the protectors of our democracy, we simply can not allow this to happen.
"So my message to Parliament this weekend is simple: It is time to forget the games and do what is right for our country".
Meanwhile, Downing Street said it is "extremely concerned" over reports that a plot has been launched to wrest control of the legislative agenda away from Mrs May if her deal fails.
The Prime Minister faced calls from a predecessor, Sir John Major, to revoke Article 50 to halt Brexit - as he warned it would be "morally reprehensible" to crash out without a deal.
Labour is also set to vote against the deal, but leader Jeremy Corbyn has resisted growing calls from within his own party to get behind another European Union referendum, insisting a general election is still his top priority if the deal is rejected. Every single household - rich or poor - would be worse off for many years to come.
He added that a "new process" of national consultation was needed, adding: 'No true democracy should deny a considered choice to its people'.
"If it means that at a general election I lose my seat because of it, that's fine".
Mrs May was boosted yesterday by two Tory backbenchers - her former policy adviser George Freeman, and Trudy Harrison - indicating they will back her deal.
But she also warned that the United Kingdom risked crashing out of the European Union with no deal or not leaving the European Union at all if MPs refused to back her.
'We'd be in a stronger position, then, to continue the negotiations as an independent third country'.