...I'd seek a bi-partisan compromise to completely revise the laws (not happening in Washington currently, obviously).
Among the things I'd look to do:

Remove existing laws making entry illegal, unless criminal acts or intent could be shown.

Establish some sort of quota for entry.

Decide what's necessary to actually 'secure the border,' and work that out with Mexico.

Decide what form 'asylum' would take and implement it.

Deport all criminals here illegally.

Develop a process which would enable those currently in-country illegally to obtain citizenship.

Improve relations with Central American countries and offer a carrot-and-stick approach which would reward them for democratization, improved standards of living, and decreased crime with large amounts of foreign aid.

Just a few thoughts...