Negotiations between the two sides have focused on the proposals for a so-called "backstop" to ensure that there is no return to a "hard border" between Northern Ireland and the Republic after Britain has left the bloc.
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 Irish backstop measure, created to ensure no new border emerges between Ireland and Northern Ireland, is supposed to be temporary until a UK-EU trade deal can be agreed, and Theresa May pledged earlier this year that the arrangement would expire "at the very latest by the end of December 2021".
While the United Kingdom remains in a customs union with the EU, it can not strike free trade deals with other countries like the USA or China.
But the European Union would not accept the UK's bid to put an end date on it - many Brexiteers argue an open-ended arrangement is unacceptable.
Media captionHelen Grant on the DUP: "I think they are bluffing".
Red lines: DUP leader Arlene Foster in Brussels.
Sammy Wilson, the DUP's Brexit spokesman, warned the PM was pursuing "the road to parliamentary defeat" because his party would vote against any deal that included the proposed backstop, branded a "sell-out".
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.
A negotiated Brexit, and Theresa May's survival, hinge on whether her ministers and MPs can live with this paradox.
It would in exchange keep access to the bloc's single market and customs union but no longer have a say in decision-making that would be done by the other 27 states staying in the EU.
The UK is expected to come up with new proposals as an alternative to the "backstop" put forward by the European Union - which the government has rejected, saying it would threaten the integrity of the UK.
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".
The Democratic Unionist Party (DUP) has threatened to bring down the government if the deal results in new barriers to trade between Northern Ireland and mainland Britain.