From Pew Hispanic [1]:

In the year following the official end of the Great Recession in June 2009, foreign-born workers gained 656,000 jobs while native-born workers lost 1.2 million, according to a new analysis of U.S. Census Bureau and Department of Labor data by the Pew Hispanic Center.

As a result, the unemployment rate for immigrant workers fell 0.6 percentage points during this period (from 9.3% to 8.7%) while for native-born workers it rose 0.5 percentage points (from 9.2% to 9.7%).

There's more at [1], including how immigrants - especially Latinos - saw their wages fall. Most importantly, there's this:

Over the two-year period from 2008 to 2010, second quarter to second quarter, foreign-born workers have lost 400,000 jobs and native-born workers have lost 5.7 million jobs.

Note that they aren't breaking immigrants/foreign-born down by status; however, a good number of those are in fact illegal aliens. Certainly, there's to an extent a difference between the job categories that illegal aliens fill and the native-born fill, and a company might have more of a need for the 300th fruit picker than another company has for the 300th accountant. However, many of those jobs that the foreign-born are doing could have been done by Americans instead, and with a net gain to the economy; see this.

If you don't like the statistics above, follow the plan.

[1] pewhispanic.org/reports/report.php?ReportID=129