The Great Recession has greatly reduced employment in industries that employ large numbers of undocumented workers (e.g. construction). The result has been a decline in the undocumented population of the United States and in particular Colorado, where the number of undocumented individuals has fallen about 25% (from 240,000 to 180,000) in the three years since 2007.
About 28% of foreign nationals in the United States are undocumented, and about half of undocumented foreign nationals in the United States are Mexican nationals.
Updated February 3, 2011:
In Colorado, the undocumented immigrant population is about 3.6% of the total population.
Nationally, about two-thirds of undocumented immigrants are in the labor force, which would imply about 120,000 people in Colorado. There are 2,665,200 people in Colorado's civilian labor force. So, undocumented immigrants make up about 4.5% of Colorado's labor force.
A crude estimate that assumes that reducing the undocumented immigrant labor force percentage by one percentage point would reduce Colorado's unemployment rate of 8.8% is almost surely wrong, however. In part, this is because undocumented workers generate jobs, both by creating firms and by consuming goods and services and paying taxes that generate jobs, as well as filling jobs. In part, this is because undocumented workers have skill and abilities that aren't present in the general labor force to the same degree, and because employers won't necessarily be able to connect their jobs to unemployed people in Colorado generally. In part, this is because some undocumented workers are themselves unemployed. In part, this is because some jobs done by undocumented immigrants are done at below market rates that are a result of their undocumented status (e.g. getting paid "under the table"), and some of those jobs wouldn't be economically viable at legal labor market rates.
It is quite probable that reducing the undocumented immigrant labor force would reduce unemployment somewhat for other workers in the labor force, but it is hard to estimate what magnitude that effect would have on the unemployment rate.
Probably the best way to estimate that effect would be to do a regression analysis that compared unemployment rates to the percentage of the labor force in each state or region that was comprised of undocumented immigrants. Given the high rate of unemployment across the nation in states with very different rates of undocumented immigrant participation in the labor force, the impact must be fairly modest.
A more sophisticated and more accurate analysis might look instead at undocumented immigrant participatioon in the labor force by both industry and region and do a regression that way (since the mix of industries in a region strongly influences its unemploymenmt rate and the involvement of undocumented immigrants in the labor force varies greatly by industry).
I suspect that this kind of analysis would reveal that undocumented immigration makes a pretty modest contribution to unemployment in the Rust Belt, where manufacturing is dominant, or in the farming states, but makes an appreciable difference in states where the construction industry and hospitality industries are a larger share of the economy, like Nevada.