Illegal Immigration: Do we build a wall?

With our recent talk of illegal immigration, there has also been talk of solutions. One current solution proposed is building a wall along our border.
Nancy Pelosi argues that building a wall would be expensive and also split communities. She says that we should be able to protect our borders without the use of a wall. Jeff Corwin also talks about the environmental impacts such a wall could have. Many species migrate across these borders so some of these species could be driven to extinction. The Los Angeles Times says that building a wall would hardly stop illegal immigration. People would find new routes or come into the country legally but stay illegally. They also add that this would not stop illegal immigration from Asia which is greater than that from Latin America.
On the other side, Pete King thinks that a wall is necessary because of the death toll that illegal immigration can have. Matt Mayer refutes the point comparing it to the Berlin wall. He says the Berlin wall was made to keep people in whereas the border wall would be to keep people out. Additionally, he adds that a weak border could be a possible entry point for terrorists. To those that say a wall would be too expensive, the Federation of American Immigration Reform says that the costs would be paid for because of the decrease in spending used on illegal immigrants. The wall would pay for itself after a couple years even if the wall only stopped 5% of immigrants.
Would a wall help? Would its benefits outweigh the costs or vice versa?