She added that Northern Ireland was not being offered the "best of both worlds".
British and European Union negotiators are understood to have agreed in principle to an all-UK backstop plan to avoid a hard border in Northern Ireland that would remove the final major obstacle blocking a withdrawal agreement.
Mrs May is expected to chair a meeting of her most trusted Cabinet members on Thursday in order to finalise her backstop plans before sending them to Brussels.
On Wednesday evening, DUP MPs abstained in a minor agricultural vote in Westminster to show they are not afraid to strong-arm the Government over proposed plans for the Irish backstop.
He added: "When we entered into the confidence and supply arrangement with the Government, we did so to enable it to deliver on the fiscal elements of its domestic programme and the referendum result to leave the EU".
The news comes after the Democratic Unionist Party threatened to vote against the Budget, and potentially bring down the Government, in opposition to a backstop plan that would treat Northern Ireland differently to the rest of Great Britain.
Wednesday is World Mental Health Day
One of these is the pressing question of mental health and how our population is coping with it. The commission also recommends increased investment in mental health globally.
The nature of those criteria, and additional language to be used about the future deal, required by the United Kingdom to assuage concerns about the ultimate need for such a backstop solution to avoid a hard border on the island of Ireland, are still open to debate. It must be one of the worrying questions for Downing Street. The Government has said it will publish revised proposals for the Irish border "in due course".
It came as Mrs May's "inner cabinet" was briefed last night on plans for a no-deal Brexit amid reports that progress ahead of a crucial European Union summit next week had been slower than hoped.
The issue of the Irish border, the major sticking point, was "close to being settled", it said. "That was the case on Monday and it remains the case today", the prime minister's official spokesman said.
Speaking to Sky News in his constituency of Larne on Northern Ireland's east coast, Mr Wilson said that the DUP were not going to be "bullied" or "bribed" into supporting a deal that could see Northern Ireland effectively kept in the single market or customs union.
Mrs May earlier used her first appearance in the Commons since September's Salzburg summit to urge MPs to act in the national interest and back a Brexit deal amid warnings that "decisive" progress is needed before a crunch European Council summit in Brussels next week.