While in the second they voted for the government to come back to the Commons with a plan B for Brexit within three days should it lose Tuesday's vote.
It was her second setback in 24 hours after MPs also voted to deny the government certain taxation powers in a no-deal scenario - in a bid to avoid such an outcome.
Addressing workers at a factory in Stoke, where 69.4% of voters backed Leave, the prime minister will also say that if the referendum result is not honoured, people's faith in politics will suffer "catastrophic harm".
Speaker John Bercow sparked uproar in the Commons last week after he selected an amendment from Tory former minister Dominic Grieve which attempts to speed up the process for the Government to reveal what it will do next if the PM's Brexit deal is rejected.
"What Article 50 says is: "The EU Treaties shall cease to apply to the State in question from the date of entry into force of the withdrawal agreement or" - and here's the key - "failing that, two years after the notification" so the notification was the letter that was delivered that Theresa May spoke about".
And he warned of a "growing risk" that Parliament could frustrate Brexit, following reports of "a plot" to change Commons rules to enable backbench motions to take precedence over Government business if May's deal falls. And then, in the 2017 General Election, 80 percent of you voted for MPs who stood on manifestos to respect that referendum result.
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.
Britain is now scheduled to leave the European Union on March 29, 2019, two years after the Article 50 process was set in motion by the European Union and United Kingdom government.
The heads of state and government said at a recent summit that the withdrawal agreement, and the contentious backstop that a large number of Tory MPs fear will trap the United Kingdom in a permanent customs union, could be neither altered nor reinterpreted.
The Labour leader told the BBC's Andrew Marr Show that if he entered Downing Street, he would "rather get a negotiated deal now if we can, to stop the danger of a no-deal exit from the European Union on 29 March which would be catastrophic for industry, catastrophic for trade". A narrower defeat and the bloc may look at fresh ways of making the agreement more palatable to get it across the line in Parliament.
Mr Corbyn warned the Prime Minister she faces a vote of no confidence in her Government "soon", saying people should "see what happens" on Tuesday, but added that his party would table a confidence motion "at a time of our choosing".
Meanwhile, London mayor Sadiq Khan has written in the Observer suggesting that Mrs May should step down and call a general election if she loses next week's vote.
"I still think that passing this deal is the responsible thing to do".
Despite her forceful words, May is likely facing a defeat - her bill is unpopular with both pro and anti-Brexit MPs.