Besides the Irish border issue, the key areas still to be negotiated are the geographical indications of products and the governance of the implementation of the deal.
His comments came after a translation of a speech given by European Union chief Brexit negotiator Michel Barnier sparked confusion about the state of play in negotiations.
However, a small Northern Irish party which supports May's minority government in the Westminster parliament vehemently opposes any checks between the province and the rest of Britain.
Arlene Foster, the DUP leader, noting how the PM was also a Unionist, said: "What is important for us is to say to her very clearly that any impediment on the two-way access in the United Kingdom single market would not be good for the Union or the economy of Northern Ireland".
However, Mrs Foster said the EU's proposals would place "an effective one-way turnstile" between Northern Ireland and the rest of the UK.More news: Home for good: Yankees eliminated by rival Red Sox in ALDS
His constituency contains the port of Larne, identified by European Union chief Brexit negotiator Michel Barnier as a place where checks on animals and animal products from Great Britain into Northern Ireland could be intensified in order to prevent a hard border with the Republic of Ireland.
He added: "If they (the government) decide to cave in to the unreasonable and unnecessary demands which are being promoted by Brussels, then we will have to consider whether or not they have kept their side of the bargain".
As that departure date creeps closer, pressure on May from various directions is intensifying.
He added that the DUP could vote down the Budget but still support the government in a confidence vote, as long as it changed its approach to Brexit.
In May's own Conservative party, some eurosceptic lawmakers want to vote against her approach to exiting the European Union as it would not bring a sharp enough break from the bloc in their view. She needs to keep either her own party onside or attract votes from the main opposition Labour Party. Michael Russell will be there representing the Scottish Government and is expected to once again sound the alarm about the damage to Scotland's economy a hard or no-deal Brexit would do.
Labour demands that Britain retain "the exact same" perks it now has within the EU's customs union and single market - something May's so-called Chequers plan does not meet and which the EU rules out since London made a decision to leave both.