Here's a helpful analogy. Think of a two-lane country road with a 20 MPH speed limit. Over time it grows to an eight-lane divided highway, with multiple cloverleaves, on-ramps, side roads, and even HOV lanes. But the speed limit is still 20 MPH. Naturally, everyone breaks the law and speeds. To enforce the 20 MPH limit, you'd need a traffic cop every 50 feet. You could do it, if you had an unlimited budget for traffic cops. But why? The rational answer is to raise the speed limit to match the road and traffic conditions. Then you'd need a traffic cop only every few miles, if that.
Our immigration laws are like that country road-turned-superhighway. The "speed limits" - meaning the visa quotas and categories - were designed a long time ago and have not kept up with the way people live, work, study, travel and love.
Yes, we could "enforce the laws on the books," as they are today, but that would be precisely the most difficult, the most expensive and the least productive approach to the problem. A better approach would be to first modernize our quotas and visa categories, then legalize the bulk of our undocumented population, and last, but not least, "get the border under control." But note: the more our immigration laws make sense, the less money we'll have to spend enforcing them.
Border control will be most effective - and least expensive - when our immigration laws look like they were written in the 21st century, rather than the 19th.