Here are a few articles:

• From the NYTimes via TruthOut:
  Illegal Immigrants Are Bolstering Social Security with Billions
  
• A report on DC
  Civic Contributions: Taxes Paid by Immigrants in the Washington, DC, Metropolitan Area (We know that's not exactly what the questioner wanted, but maybe it will be useful anyway.)
  
• Undocumented Immigrants in New Mexico: State Tax Contributions and Fiscal Concerns

It's past the deadline now, but I found the following documents which may be relevant. I could find nothing specific to Washington State - basically the documents found indicate no precise data (or methodology) exists on illegals and their costs. However these documents may help counterpoint any cost figures the Minutemen Project may claim.

1. Overview of why it is hard to estimate net costs of illegal aliens, balanced view, well sourced
   
2. Might be useful if this group wants to try an estimate local costs, "Local Fiscal Effects of Illegal Aliens"
   
3. "Illegal Aliens: National Net Cost Estimates Vary Widely" US GAO. 1995.
   
4. "Illegal Immigration in America: A Reference Handbook" (1999)
   
5. "" (2006)
   
6. "Illegal Aliens: Assessing Estimates of Financial Burden on California" (1994)

Library of Congress Subject Headings
Primary good one is: Illegal Aliens - United States - Economic aspects
and various other subdivisions under Illegal Aliens - e.g. Statistics, Costs, Finance