The Foreign Secretary said if the Commons crushes the deal a second time, Britain could be forced into a permanent customs union with Brussels - meaning no new trade deals.
If her deal fails to pass on Tuesday, MPs will have a chance to vote against leaving with no deal and to vote on delaying Brexit.
Writing in The Sunday Telegraph, the MPs said: "The consequences of extended uncertainty would mean political calamity for an exhausted population and a costly delay for businesses which have prepared to exit on 29 March".
Nigel Dodds, the deputy leader of the Democratic Unionist Party (DUP) which props up May's minority government, and Steve Baker, a leading figure in the large eurosceptic faction of her Conservative party, warned "the political situation is grim".More news: Protesters Go On Feminist Strike in Madrid to Celebrate Int'l Women's Day
The Sunday Times said May was battling to save her job as aides were considering persuading her to offer to resign in a bid to get the deal approved.
Unless it negotiates a delay, Britain would then be on course to leave the European Union after 46 years of membership with no plan on March 29, causing huge disruption on both sides.
At the heart of the House of Commons's opposition to the already-negotiated divorce deal is the so-called "backstop", a provision to keep the sensitive Irish border open after Brexit, which the eurosceptic wing of Mrs May's Conservative party fears could trap the United Kingdom in the EU's trading rules forever.
The current deal took 18 months to negotiate between the EU and the United Kingdom and May has been seeking concessions from her European counterparts on the backstop issue to help get it through the Commons.More news: Aware that Nirav Modi is in United Kingdom , extradition requested
But, May's attempts to get the clause rewritten have so far failed to yield any result, with European Union negotiators unwilling to meet her demands, and Britain rejecting a compromise offer.
Their intervention comes as MPs prepare to vote on May's deal on Tuesday, two months after her deal was roundly rejected by 230 votes in January.
If her deal is rejected, lawmakers will be able to vote on Wednesday and Thursday on whether they want to leave the bloc without a deal or ask for a delay to Brexit beyond March 29 - all but wresting control of Brexit from the government. If the deal is rejected, the parliament will then vote on a no-deal scenario.
The ComRes poll was commissioned by pro-Leave group Brexit Express which surveyed over 2000 people and found that 76 percent of people also believed the Government had handled negotiations poorly. "Those carrying additional inventory know an extension will squeeze their cashflow for longer".More news: Second man cured of HIV