I don't see the UK PM defining Brexit according to Trump's dangling of an American trade deal. Trump isn't a reliable enough actor to make anything conditional upon him. And he has launched a trade war against the UK, amongst others.
For myself, I want a harder Brexit and trade deals with our commonwealth partners as the first port of call. Once we have those, then we talk with the US.
But even if Trump is on the side of a hard Brexit, I am not comfortable with a US President intervening in our decisions. Didn't like Obama's back of the queue comment either, which was far less disruptive.