It was a line that worked because enough people said "We want a secure border" and the response from their government (on both sides) was "You're an idiot."
OTOH, logistics aside, what is the wrong message about a wall? I don't care if we do it with carrier pigeons and soap bubbles or strongly worded letters or laser guided piranhas: If you're not legally allowed to enter our country you can't. It's not just an argument about HOW we do it. The argument has been if we should do it at all,
Robert answered your other points, so I'll just deal with this.
This is the whole cognitive dissonance thing at work again. People want to believe a narrative that the Leftie president is soft on immigration and has allowed open borders, but the fact of the matter is that
Obama has deported more people than any other President in US history, and
more people than all of the Presidents of the 20th century combined. And he's done so with a focus on priority one deportees with criminal records rather than families (and
no, that does not mean illegal immigrants are more prone to committing crime than US citizens, unlike what Trump would have us believe). If you're some hardass anti-illegal immigration person, than you should be delighted by Obama, who has always been decidedly middle of the road politically despite being depicted by Republicans as slightly to the right of Che Guevara.
Furthermore,
net immigration from Mexico was zero (or a loss) for most of Obama's administration for a number of reasons, so people thinking there's some massive invading horde of immigrants pouring over the borders ready to steal all your jobs are equally delusional.
So, we already have a border that is secure and well-maintained, an immigration service which is deporting more people than ever before, more undocumented immigrants are leaving than coming in, and the "Mexico's sending us their rapists, drug dealers, and criminals" line is a racist myth. Yet to hear Trump talk we're one step away from needing el Glotónes to fight off a Mexican Red Dawn.
We're not repelling the Picts or Mongol invaders, we're not defending France with fixed defenses in a mechanized and mobile age, and we're not preventing East Berliners from leaving a totalitarian state. Mexican immigrants are just looking to better their lives and take care of their families. They're not stealing jobs that the average American is seeking, they're not committing crimes left and right since that would lead to you getting... wait for it... deported, and they're not secretly helping ISIS invade America, or else Obama, the founder of ISIS, would stop deporting them. It's not World War Sí and we don't need a logistically impractical, fiscally wasteful, bigoted in conception, and easily circumvented wall to defend ourselves from an invasion that's not happening.