Mayor Bill White (who is expected to challenge for the governor's mansion in 2010), originally signed off on the city participating in ICE's 287(g) program in which city jailers would become de facto immigration officers and would screen for those suspected of being in the country illegally. Critics of 287(g) say that the program is nothing more than legalized racial profiling.
Now I believe that if you're going to another country you need to keep your nose clean and follow the law -- and if these programs were directed at individuals who were found guilty of criminal offenses, I would have no problem with their being deported from the country. My problem stems from the fact that when an individual is arrested and taken to jail, that individual is still innocent unless proven guilty.
The Bill of Rights doesn't use the word "citizen" when spelling out the measures to protect us from the overreaching arm of the state. You can check it out.