He said a solution for the border won't really be needed until the end of the Brexit transition period on January 1, 2021 because the United Kingdom will effectively remain inside the customs union and single market during this interim phase.
With Labour, the Lib Dems and the SNP, plus a handful of Tories, in favour of remaining in some form of customs union after the United Kingdom leaves, the government is at risk of potential defeat when the defining vote is held next month.
The EU's chief Brexit negotiator has told businesses to prepare for the possibility of the United Kingdom exiting the bloc without a transition period amid a stalemate over the Irish border issue.
He said he hoped to get off to a "racing start" by implementing new trade deals quickly with countries like Canada after December 2020 - when the transition period will end.
It suggests that the United Kingdom accepts it may have to agree to an unpalatable backstop plan for keeping Northern Ireland - and possibly the whole United Kingdom - in many parts of the customs union and single market rules indefinitely.
Mr Davis said he would always "try and make myself available", but blamed the fact he was working at "the maximum pace" possible with Brexit negotiations ongoing and the government's flagship Withdrawal Bill facing a rough ride in the House of Lords.
The main issue here is that we don't want to be any closer to the European Union than any other Country in the World, as we need free trade deals with all Countries.
Lawmakers will have to decide whether to back the government or reject the agreement - with the risk that Britain could crash out of the European Union next year without any deal in place.
While there were "hard issues" involved and the process would not be "straightforward", he said the situation was not "as difficult" as many people were trying to make out.
Committee chair Hilary Benn said this was "not satisfactory" as the sessions were "very important" to MPs.
The EU Withdrawal Bill returns to the Lords on Wednesday for a third day of report stage debate, which is when all the voting action happens.