So you're in essence saying a wall will work. It will force people to seek alternative places and methods to cross. Places and methods the border patrol will be prepared to interdict. The barriers assist the border patrol and are a force multiplier.
But it will also be necessary to change our laws, to criminalize visa overstays and provide expedited deportation procedures of all illegals.
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I agree with both your points.
A wall will force or persuade people to seek an easier crossing. I think it's becoming pretty clear that there isn't going to be 2000, or even a 1000 mile mall completed. At most it will end up being about 200 mile of slatted fence with 1800 miles of reinforced fencing, cattle fencing, electronic monitoring, and aerial surveillance. Even if the "wall" were extended to 2000 miles, it wouldn't stop half the illegal crossing because most illegal entries will be at ports of entry. Less than 1% of vehicles are searched and only a small fraction of a percent of containers, boxcars or private planes are searched. Almost all of these searches are for drugs, not people.
Yes, reducing visa overstays, will require changes in the laws but it will also require a tracking system, and cooperation from sanctuary cities and states. In order to get changes in immigration laws needed to significantly reduce the number of illegal immigrants in the country, democrat votes in congress are going to be needed, and that's not going happen without changes that republicans are not going to like such sharp increases the number of temporary work permits and increased country limits.