A free market, classical liberal approach to the problem of illegal immigration would require a limited effort by the federal government, without unduly burdening the states and the people.
Free market economist Milton Friedman blasted the overgenerous welfare state far more than the mere presence of illegal immigrants in the United States. Do not blame unscrupulous employers exclusively or the teeming masses longing for political freedom. Public services at public cost create the greatest draw for illegal immigration. Limit the handouts, and fewer individuals will find support for themselves. As Governor Romney suggested in Florida, they will then just leave.
Newt Gingrich commented that elderly illegals would not leave the country -- yet their entrance and presence in this country does not comprise the greatest burden to this country.
Add to the reduction of easy handouts from the public sector, a streamlined program that provides a means for employers to verify the status of prospective workers, and illegal immigration will slow to a trickle. Of course, verifying the employment status of an individual must remain within the reins of the state as much as possible.
Beyond deterring illegal immigration, the United States must also streamline the naturalization process -- make legal immigration easier. A resident of India, for example, has to wait an average of thirty years before becoming naturalized. The federal government must also suspend quotas restricting migration from different parts of the world.