Arlene Foster says it has "raised alarm bells" as Mrs May appears "wedded to the idea of a border down the Irish Sea".
She spoke out after "frank" exchanges with Cabinet Office minister David Lidington on the differences between the Scottish and United Kingdom governments over their approach to exiting the European Union (EU).
Ever since her botched gamble on a snap election in 2017 lost her party its majority in parliament, May has relied on the DUP to govern.
Appearing on the Matthew Wright show, Mick Fealty, the editor of Northern Ireland-based political blog, Slugger O'Toole, said Irish businesses were anxious.
Mr Varadkar said he believed the negotiations were at a "sensitive point", and while a successful outcome is not guaranteed a deal is possible in next few weeks.
That "something" - a "backstop to a backstop" - is a return to the original EU proposal which would see Northern Ireland in a European customs union and would mean a customs border in the Irish Sea.
A senior source said: "It does not feel to me like things are going to move today".
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Minister for Justice Charlie Flanagan said the issue of British Prime Minister Theresa May writing to the DUP was an internal United Kingdom matter, but said there was a real deep feeling of uncertainty among communities with regard to the border.
Mr Varadkar went on to say that his objective on trade was to "avoid the emergence of any new borders".
Any version of the backstop would apply unless and until a wider UK-EU deal on the future relationship solved the issue of how to avoid a hard border with the Republic.
"She has sent us where she believes she is now at, and remember this is before she goes to Brussels to negotiate with them on what they believe is possible, but now, as it stands, we could not support her proposals".
A potential sticking point could be demands for European Union fishing fleets to be given continued access to British coastal waters as the price for agreeing to Mrs May's UK-wide backstop, the Daily Telegraph reported.
Ireland's Taoiseach Leo Varadkar, Mrs May's effective deputy prime minister David Lidington, and Northern Ireland Secretary Karen Bradley were attending a summit in the Isle of Man.