They do travel through the border, but we have to have limitations, especially when we allow people in from countries that hate us like Middle Eastern Countries. You are right that most do the jobs we don't want, and that's a very good reason why Amnesty should be granted to those that are here and in good standing. But letting more in, does not mean there will be more police and firefighters, that's if you're trying to say "if we allow more in, there will be more violence, therefore more police are needed" because there is no correlation with crime and immigration.
http://www.time.com/time/nation/article/0,8599,1717575,00.html
Immigration: No Correlation With Crime
Despite our melting-pot roots, Americans have often been quick to blame the influx of immigrants for rising crime rates. But new research released Monday shows that immigrants in California are, in fact, far less likely than U.S.-born Californians are to commit crime. While people born abroad make up about 35% of California's adult population, they account for only about 17% of the adult prison population, the report by the Public Policy Institute of California (PPIC) showed. Indeed, among men ages 18 to 40 — the demographic most likely to be imprisoned — those born in the U.S. were 10 times more likely than foreign-born men to be incarcerated.