There are nine congressional districts along the US/Mexico border. All of them have representatives who oppose a border wall from sea to sea. Many of them are willing to discuss notions of ‘border security’ but are careful to point out that the wall is not border security.
Will Hurd is interesting as the only Republican of the nine as well as the representative that has the longest stretch of border. His district also has some of the most remote and desolate places. The article below describes reasons behind his views including impacts on local communities and overall effectiveness.
This was modified the following year by an amendment added to the 2007 appropriations bill. The sponsor was TX Senator Kay Bailey Hutchison and co-sponsored by all the other senators of states along the Mexico border (TX, NM, AZ, CA), five Republicans and three Democrats in total.
The amendment gave DHS much more leeway on how the border might be secured and also said DHS needed to consult with local communities along the border.
A good example of how if you don’t have local support, something that looks attractive on TV may not really happen the way you expect.
Building a border wall will likely involve taking private land, potentially a lot of land. When the landowners don’t want to sell, the government can invoke eminent domain.
The following site provides background of what happened in one such famous case of Kelo vs. New London. The outcome of that case also strengthened a backlash and potentially eminent domain laws in the US.
These delays and now rescheduling might have an effect in both direction. An asylum seeker, perhaps with a not very strong case, might stay even longer in the US before a judge denies an asylum request. An asylum seeker with a strong case might have have that case become less strong, e.g. if they were providing for a sick dependent who then dies.