The UK government has been clear on three aspects of Brexit: (1) that the UK is leaving the Customs Union; (2) that there is to be a frictionless border with Ireland; and (3) through its electoral pact with the DUP, that NI is not to be treated differently from the rest of the UK.

The problem for the UK government is that these three aspects are logically inconsistent. Any two aspects can be satisfied at once, but not all three

Yesterday, the PM came unstuck in the negotiations because she managed to get balls (1) and (2) in the air ie the UK could leave the Customs Union and have a frictionless border with Ireland, because NI would stay 'aligned' with EU regulation - but that left the PM holding (3), and the DUP said 'no'.

Nicola Sturgeon and others suggest the solution is for the whole of the UK to stay in the Customs Union - that gets (2) and (3) in the air, but the government has to drop (1) - and that would seem politically impossible.

Brexiteers seem to suggest that the PM drops (2) - allowing a UK/EU hard border in Ireland, but then ameliorating the effects using technology and the free trade agreement. That will, at least, disappoint Ireland and, at most (and worst), see a failure of the NI peace process because it fundamentally undermines the Good Friday Agreement. 

See further comment here: