Politicians insist that the success of comprehension immigration reform is dependent on securing the borders. Some honestly believe that the government can initiate efforts on the border that will completely shut off the spigot of unauthorized immigration. But most politicians realize that any efforts to secure the border can at best decrease the number of unauthorized immigrants who will cross the border (even though they normally don't care to admit so in public).
It's easy to see why a "secure" border is nothing more than a pipe dream. Even if the government spends billions of dollars to erect a fence on the border, immigrants can, as a New York Times article pointed out, use "ladders rented out for $35 a climb" to get over the border fence. Immigrants can also arrive by sea, or through tunnels dug under the border, or by sneaking past a border checkpoint in the back of a truck.
As I write these possible means of transportation, you may be brainstorming ways to combat them. Indeed, there are many ways to combat them. But two problems emerge. First, the government will never spend the resources needed to combat them all; doing so would be cost-prohibitive. Thus, there will always be weak links in the chain that border-crossers can exploit. Second, the government will not impose security measures that severely impede the economy. A more thorough check of every piece of cargo that comes into the United States may catch more people, but overly excessive constraints on commerce will never fly. So at least with the current technologies and resources available to the United States, complete border security is a laudable but unrealistic goal.
Politicians' focus on border security also fails to appreciate the cause of a significant percentage of unauthorized immigrants, namely those who legally entered the United States but did not leave when their authorization to remain in the U.S. expired. Surprisingly, the government does not have a good system in place to check to see if these individuals actually left the country. So even though many such unauthorized immigrants fly under the radar, politicians hone in on the actual border with laser-like focus, trying to convince constituents that they can completely solve a problem which can really only be reduced, while forgetting that border security is only one piece of a much larger puzzle.