I go back to the last Fox debate (I think... they all blend together after awhile) where he was specifically asked about the EPA and drug subsidies. Fox had graphics that showed his numbers were... unpossible, to put it lightly. He talked around it.
I bring that up to say that he cannot deliver on what he is promising, even if he could do it in a legal sense. And I'm not sure he can, without a constitutional crisis, which may also be part of his thinking.
Private businesses typically have a strong executive in terms of powers. Trump, most certainly, is a strong executive. He would probably do everything he can to make the presidency a strong executive. But, is that what we really want?
I don't watch the debates (I don't find them to be informative; they're more like circus entertainment), but part of the (legitimate) criticism about Trump has been a lack of detail. Trump has never been a politician, and has had to learn as he goes. Part of that learning curve is understanding that you have to be able to provide basis-of-design specifics at a stage where, in business, you're only at the project feasibility stage. I think he's gotten better on that point, and has much room for further improvement.
As for funding the wall specifically: I think Trump is referencing the sheer volume of money that gets wired to Mexico from the US every year. (At least, I think that's really what he's talking about with respect to a trade deficit.) The wall could be funded over ten years simply by imposing a tariff those wire transfers (remittances):
Donald Trump Plans to Impound All Remittances to Mexico -- Would That Even Be Possible? | National Review Online
I have no problem with a strong executive - provided that such executive acts within the bounds of the constitution and law.