A wall would help a little, but a large proportion of illegals enter legally and then overstay their tourist/student visa. A wall would just shift the problem so that more would enter legally and then just not leave, unless we also included better enforcement against criminals who stay here illegally and their criminal employers.
A 20 moratorium on visas issued to Mexicans. Problem solved.
You are correct, we do need a better enforcement against criminals who stay here illegally and their criminal employers
Immigration from one country, Mexico, is 2.5 times that of many countries combined.
I've taken the figures from the above table at cis.org and graphed them.
Note the sharp increase in immigration from Mexico and how that differs from all other regions' increase. Note also the sharp decline in immigration from Europe while all other regions have increased.