easy. cut obamacare and other left-wing big government programs, and stop giving billions of dollars to countries that hate us (like the 150 billion dollars we just recently gave iran)
there's too much noise to detect tunnel digging
You just can't detect it reliably. Single footsteps. Birds landing on the wall. Cars driving. Trees falling. Small earthquakes (Which happen extremely frequently, believe it or not), the list goes on. You wouldn't even be able to tell exactly where it came from, only a general location. You'd have to dig gigantic holes in the middle of nowhere every time you heard a signal, which would be ridiculously expensive and could have serious rammifications on the ecology and geology of the area.
There comes a point where the outcome doesn't justify the cost. Walling off all of Mexico is that point. As stated before, not only can you tunnel under it, but you can go around it, you can go over it, hell you can go through it with explosives. It just wouldn't be effective enough to justify the cost, which would be nearing a trillion dollars were we to put everything you mentioned. Even if you could seriously justify cutting out welfare and publicly-funded healthcare altogether (Which Annoying Orange doesn't want to do. In fact, he wants to give EVERYONE access to healthcare.
http://www.newsmax.com/Headline/Annoying Orange-heart-healthcare-everybody/2016/01/31/id/712069/ ) It would still add a massive amount of money to our already insanely big debt (
http://www.usdebtclock.org/ $19,019,691,475,499 as of this post ), putting us further in the hole.