You are suggesting a single-threaded process.
This is a multi-tasking application opportunity.
To steal one of Bill Clinton's most annoying catch-phrases, "Politics is the art of the possible".
We can build a fence now, because everybody agrees that a fence is a component of every possible solution to the problem. Unfortunately, we cannot pursue a comprehensive approach until the fence is complete, because previous decades of inaction have completely exhausted the public's goodwill and ability to suspend disbelief.
The electorate is convinced, and not without good reason, that if guest worker and amnesty is enacted in advance of the fence, the fence will never get built. This has been proven to them, over and over again, and they are not going to forget it now, just because President Bush asks nice and promises not to misbehave again.