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).
Without DUP support for a deal, May will have much less chance of getting her deal through parliament.
She added that Mrs May "will have a job of work to do to get this through cabinet".
Culture minister Jeremy Wright's comments come after Prime Minister Theresa May's Westminster allies threatened to pull support for an agreement if Northern Ireland were separated from the United Kingdom via a customs border down the Irish sea.
Tensions between Mrs May and her DUP allies have been exposed amid concerns about measures aimed at avoiding a hard border on the island of Ireland.
"That is why we're seeking on that is legally operative and one that gives us that guarantee that is necessary".
"There is no clean break here, Brexit is going to go on for a very long time".
"And we'll do our best to work through it and make sure we get the best outcome for our citizens".
Brexit was top of the agenda and it dominated questions at the press conference afterwards - following that leak of the PM's letter to the DUP.
Mr Varadkar pointed out that the DUP don't represent the majority of people in Northern Ireland.
"We want to stick to the confidence and supply arrangement [with May's government] but you know there are two sides to that and the government has obligations under the confidence and supply arrangement as have we", Wilson said.
"My objective when it comes to trade is to do everything we can to avoid the emergence of any new borders among any of us", said Mr Varadkar. "But Brexit has given rise to a hard situation and we need to resolve that".
The European plan, known as the "backstop to the backstop", would leave Northern Ireland tied to the single market and customs union if Brexit talks collapse.
DUP leader Foster said in a letter to May that any backstop could not leave Northern Ireland aligned to specific sectoral European Union market regulations.
The DUP accused May of breaking a promise that that she would never sign up to a deal that treated Northern Ireland differently from the rest of the UK.
London's latest political spat underscores the trouble May's fractured government faces in passing through parliament any Brexit arrangement it thrashes out with Brussels over the coming days.
Arlene Foster says it has "raised alarm bells" as Mrs May appears "wedded to the idea of a border down the Irish Sea".