The UK would collect tariffs set by the EU customs union on goods coming into the UK on behalf of the EU.
"They do literally plunge a knife into the heart of government and particularly to the Prime Minister - because it is very much her fixed view, and that is what we stood on at the last election".
However, the environment secretary also expressed scepticism about the merits of an alternative customs proposal, saying the customs partnership model had flaws and needed to be tested.
One group will consider a "customs partnership" whereby the United Kingdom would collect tariffs on behalf of the European Union, but would remove the need for new checks at the border. However, it has been denounced by Brexiters who say it is untested and would force Britain into copying the EU's product standards and regulations. Max fac or maximum facilitation accepts the need for a customs border, including in Ireland, and depends on the development of technology to make it as frictionless as possible.
"The critical thing is to meet that deadline".
Gove said the cabinet agreed that neither of these two models was absolutely flawless.
Speaking on the same programme, Ireland's tánaiste and foreign minister, Simon Coveney, said there had been a clear commitment from May that there would be no border infrastructure.
"I will need your help and support to get there". 'There will have to be compromises, ' she wrote in her article. It would also allow the government to cut tariffs on goods from other countries destined for domestic consumption.
May said she wanted to restate her case "amid all the noisy debate and technical discussions".
Labour's Sir Keir Starmer, the shadow Brexit secretary, said neither of the options would work and claimed it was "farcical" that the cabinet was fighting over them. Leader Jeremy Corbyn, a lifelong eurosceptic, has so far resisted calls to try to keep Britain in the bloc's single market, arguing that its rules would prevent him from fulfilling policy pledges including taking some businesses into state ownership.