Trump was talking out his rear when he said Mexico would pay for it. I do agree we need it, but we'll have to foot the bill. It absolutely is sticking it to the government that gets paid for the gridlock we'll endure for the rest of Trump's term.
The distinction is between legal vs illegal immigrants---not immigrants vs invaders; conflating the definitions simply muddies the waters and serves no useful purpose for discussion purposes.
There are thousands of miles of abandoned railway lines in USA (Wikipedia) where you could pick up the steel rails and use them for slats to build the wall -save a lot of money.
Citizens can mail money as "gifts to the United States," according to the U.S. Treasury Department, but it's not clear whether the Department of Homeland Security can accept gifts.
Furthermore, the money can only go into a "general fund" that must be allocated by Congress.
.... it remains unclear how the U.S. government would get the money.