I actually advise a lot of employers on immigration issues and live in an area with a very high hispanic population, both legal and illegal. I don't trust most of the statistical studies but I trust my own eyes and ears (forgive me as I speak in anecdotal generalities):
Positives:
Most of these people work VERY hard and are focused first and foremost on being productive and getting ahead financially - very "American Way;"
If illegal immigrants aren't paying taxes, in my experience it is almost exclusively the employer's choice; where the employer plays by the rules, the workers have no problem with it;
Massively anecdotal, but I speak a little (teensy) bit of Spanish and I have NEVER met a hispanic immigrant of any age or either gender in any context who wasn't cordial if not downright friendly - at work, in the park with my dog, in a grocery store late at night, on the metro;
Negatives:
Many immigrants have no desire to put down roots here or contribute to the culture on a broader scale;
As with any immigrant group, some struggle and some of those who struggle turn to crime, petty or violent;
Those little stickers on the back of Totota 4-Runners with Calvin peeing on a Ford logo
If every illegal immigrant in the Mid-Atlantic disappeared tonight, tomorrow the construction labor, industrial cleaning, restaurant, landscaping, hotel and farming industries would be decimated. Fact (anecdotal, sure, but fact). DC United would also have 3 fans per game.