West Midland MPs Dame Caroline Spelman and Jack Dromey have insisted they are not trying to block Brexit, despite supporting proposals that could mean it is delayed.
They are backing plans to delay Brexit for up to three months if there is no withdrawal agreement in place by March 13.
But their said their goal was simply to prevent a "no-deal" Brexit, which many employers including Jaguar Land Rover say would be a disaster for their businesses.
Writing for Birmingham Live , the two MPs said their proposal "would not stop Brexit, decide what kind of Brexit we should have or what kind of deal would work.
"It doesn’t affect the result of the referendum ... nor does it take responsibility away from the Government to propose the way forward."
But they said: "However, if a delay is required to get a deal that works in the interest of our region and the country, this is something which must be considered."
British carmaking had become "a world-class success story", the pair said, but they warned: "All this is at stake through a No deal Brexit".
And they said representatives of one "major, international car company" had reported that their board "now sees the UK as the ‘problem child’ of Europe."
Mr Dromey is Labour MP for Birmingham Erdington and Dame Caroline is Conservative MP for Meriden. Both MPs have major Jaguar Land Rover plants in their constituency.
The UK is currently due to leave the European Union on March 29, but there is currently no withdrawal agreement in place.
An agreement would mean there is a transition period until December 31 2020, during which the UK remained part of the EU's customs union and single market. This would allow trade to continue without restrictions.
During the transition period, the EU and UK would attempt to agree a permanent trade deal.
However, if we leave with no withdrawal agreement then all our current trading arrangements with the EU will end.
The EU and UK would still be able to trade, but firms would have to pay costs called tariffs, and there would be delays at borders.
This would be a particular problem for manufacturers including carmakers, because many of them import parts from a number of different suppliers from across the EU.
Mr Dromey and Mrs Spelman are working with Labour backbencher Yvette Cooper and Tory former minister Sir Oliver Letwin to propose legislation that could mean the UK fails to leave the EU on March 29 - if there is no deal.
The plan is to set the Prime Minister a deadline of March 13 to convince MPs to support a Brexit withdrawal agreement.
If she fails, then Mrs May would be forced to bring a motion to Parliament setting out what she plans to do next.
And she would have only two choices. One would be to delay Brexit.
The second option available to Theresa May would be to say the UK should leave the EU with no deal.
But if she chose this option then MPs would hold a vote on her proposal. And if they voted to reject a no-deal Brexit, then the Prime Minister would be forced to delay leaving the EU whether she wants to or not.
The plan is set out in proposed legislation. If it becomes law then the Prime Minister would be legally obliged to do what it says.
Ms Cooper has said she will begin the process of introducing the legislation on February 26, if no deal has been agreed by then.
First of all she will ask the House of Commons to agree that time should be set aside to discuss her proposed law. If it agrees then MPs will hold debates and a series of votes that could bring it into effect.
