Any additional vote would take at least five months to prepare meaning even if one were announced next month, Britain would not be ready to leave the European Union as planned in March 2019, research by University College London (UCL) found.
The EU says there needs to be major progress at a summit in Brussels next week if the two sides are to strike a divorce deal before Brexit day.
Trade secretary Liam Fox told friends that her proposal "would make life very hard for me", according to a Mail report, because it would limit the UK's ability to strike new free trade deals outside the EU.
Sammy Wilson said: "It was a way of reminding the government that while our vote wasn't important last night, it would be important some time in the future and we would have no hesitation withholding it if we thought that was a necessary sanction to impose".
Brussels has suggested that in the event of no deal, Northern Ireland should stay in the EU customs union - something the United Kingdom has repeatedly rejected as it would create a new border between Northern Ireland and the United Kingdom across the Irish sea.
Sky News understands work to prepare for such a scenario is already under way, while Brexit Secretary Dominic Raab has said he is confident Britain would be able to negotiate such agreements with the likes of France, Belgium and the Netherlands.
She added that the plan for checks on goods was "a one-way turnstile, which could restrict trade from Great Britain to Northern Ireland" and said it was "the worst of one world".
"The majority of people in Northern Ireland are looking for something quite different from what the DUP is looking for, and yet the DUP is given this platform as if it speaks for Northern Ireland".
In a worrying development for May's government, one DUP source told Politico: "Right now, Labour's position is better for us than May's". A negotiated Brexit, and Theresa May's survival, hinge on whether her ministers and MPs can live with this paradox.
Downing Street also announced a further 29 no-deal notices would be published on Friday afternoon, setting out what businesses and consumers should do in the event of there being no agreement by 29 March 2019.