Writing in the Sunday Telegraph, Dodds and Baker, who is the deputy chairman of the pro-Brexit European Research Group (ERG) said any "extended uncertainty" around Brexit would be a "political calamity" and that the United Kingdom must leave the EU on the scheduled date of 29 March.
May warned on Friday that were lawmakers to reject her deal on Tuesday, it would increase the chance that Brexit never happens, leaving voters feeling betrayed.
Britain faces "total uncertainty" if lawmakers reject Prime Minister Theresa May's Brexit deal on Tuesday, health minister Matt Hancock said on Sunday, adding that he did not think a defeat was inevitable.
Many MPs are opposed to the Irish backstop, the insurance policy created to prevent a hard border in Northern Ireland by keeping the United Kingdom in a customs union with the EU.
Talks will continue in Brussels but without a major breakthrough, May looks set to lose her second attempt to get lawmaker's approval and smooth Britain's exit from the European Union, its biggest shift in trade and foreign policy in more than 40 years.
"UK will not be forced into customs union against its will".
Ahead of a vote on Tuesday on the divorce agreement struck with the bloc previous year, more than 50 businesses warned members of parliament in an open letter of the dangers of failing to unite behind a way forward that avoids a hard border and protects peace and economic progress in Northern Ireland.
Ahead of a crucial round of votes, Mrs May has issued a last-ditch plea for her much maligned deal with the European Union (EU).
However, Northern Ireland would have to remain in the EU's trade orbit to prevent the need for any customs checks on the border with EU-member Ireland.
But Brexit Secretary Steve Barclay and the DUP, the party Mrs May's government relies on for a majority in Parliament, were both dismissive of the EU's latest proposal.
He said parliament faced a choice between no deal by accident or no Brexit.
"With a very real deadline looming, now is not the time to rerun old..."
The prime minister's initial attempts to get backing for her deal failed to win approval in Parliament after pro-Brexit MPs in her Conservative Party, and her allies from Northern Ireland's Democratic Unionist Party (DUP) raised concerns over the indefinite nature of the Irish backstop arrangement.
May has been wooing opposition Labour MPs with promises of protection for workers' rights and new funds for poor towns, but the Labour party leadership remains against her deal.