Mr Davis said, if a deal of this kind is struck, it will be "very obvious" to voters at the next general election that the Government had broken promises from the 2017 Conservative manifesto and the Prime Minister's Lancaster House speech setting out her Brexit "red lines".
The radical move is understood to be one of the options being considered by the DUP if attempts to nail down a deal with Brussels include any proposals that would leave Northern Ireland being treated differently to the rest of the UK.
Despite their abstention, it was still defeated by 59 votes.
"It is something no British Prime Minister will ever agree to. Our position hasn't changed and we don't expect the Government will change its position".
German Chancellor Angela Merkel said Wednesday there had been progress on Brexit ahead of a crunch summit but warned that the "devil is in the detail".
However, Downing Street insisted that defeat on the Budget would not amount to a vote of no confidence in the government under the terms of the legislation which provides for fixed-term, five-year parliaments.
Brexit negotiators are working "day and night" to try to reach a deal, the EU's Michel Barnier has said.
LEAVE voters in Northern Ireland regard sacrificing the peace process as an acceptable price for Brexit, new research claims.
"Firstly, it is clear from our meetings that any form of border in the Irish Sea will impede access for Northern Ireland to new United Kingdom trade deals".
The joint survey by the University of Edinburgh and Cardiff University found that 87 per cent of the overwhelmingly unionist advocates for leaving the European Union believe the collapse of the peace process is justifiable if Brexit is delivered.
"Secondly, "best of both worlds" is not on offer".
British Prime Minister Theresa May and the hardline Northern Irish unionist party that props up her government reject any encroachment on British sovereignty.
He also stressed the EU's insistence that Britain must accept possible checks on goods moving between its mainland and its province of Northern Ireland, saying Brexit will trigger the need for customs, value-added tax and compliance checks with European Union standards.
To put up tariff or non-tariff barriers would be "economically disastrous", she said.
But he said a "Canada-plus-plus-plus" deal was "within our grasp with political will and imagination".
They "will not tolerate a half-in, half-out Brexit" he said, amid reports Mrs May will break the deadlock over the Irish border by keeping the EU's present customs arrangements beyond the transition period in December 2020.
Nor do we believe they are even necessary because the means for dealing with trade across borders where taxes have to be collected, different regulations have to monitored and trade measured are already in place between NI and the Irish Republic.