Randal Archibold of the New York Times offers "Border Counties Shortchanged in Immigrant Costs, Study Says" (link):

Counties along the Mexican border from California to Texas are shortchanged millions of dollars a year in costs related to prosecuting and jailing illegal immigrants, according to a study released Wednesday.

The study was by the University of Arizona and San Diego State University on behalf of the United States/Mexico Border Counties Coalition, a group representing the 24 border counties.

Cumulatively, the counties spent $1.23 billion from 1999 to 2006 to process illegal immigrants in the justice system, the study found. Federal programs offset only a fraction of those costs, and often did not receive the maximum level of financing that they are authorized to receive, the study said...

You can get a copy of the study here. The Federal government has a program to reimburse states for such costs, called SCAAP ("State Criminal Alien Assistance Program"). Looking at the PDF available elsewhere at their site indicates that those same counties only received around $60 million through that program in the same time period.

However, the use of the word "shortchanged" in the NYT title assumes that those costs should have been incurred in the first place, when the opposite is true. The NYT's implicit response is simply to increase the funding, when what should happen is the Feds should be strongly encouraged to enforce our laws in the first place.

Related:
Bush budget: more for border patrol, none to jail illegal aliens
Feds paid $2 billion/year to jail criminal aliens
"[CA] should not pay to clean up immigration"
Bush refuses to pay for the trouble he causes