"Last year's bipartisan Senate bill recognized this, and raised quotas for both family and employment-based immigration."

Sounds reasonable to me. Does that mean the real problem is that Mexicans continue to enter illegally? If so, the next logical move would be to give amnesty to those who are in the U.S. illegally, and to heavily fine employers who continue to hire illegals.

Where do 'day workers' being brought across the border figure in?

Building walls and prisons to contain people is no solution at all.