This depends on what kind of problem you are talking about. Economically, I would argue that it is not a problem. In terms of security, it is something of a problem. In terms of culture, I don't think it's a problem. Morally, it might be a real problem. In terms of how it makes many Americans feel about people of color, I think it's a real problem.
As you can see, there are many facets to this issue. Some brief points:
- Economically, studies are mixed as to the impact of illegal immigration. Illegals use services, but they also tend to pay payroll (Social Security and Medicare) taxes without being eligible to benefit. They also free Americans up to do higher-skilled jobs.
- If illegals can come over the border in such numbers, terrorists presumably could too. So the illegals themselves may not be a problem, but the fact that they can get in is.
- Some people worry that America will lose its "Americanness." They worry about the whole "Press 1 for English" thing. I don't think that's an issue because illegals assimilate too.
- Morally, having all these people breaking the law by being here may be a problem.
- Finally, this creates ill-will between white Americans and Hispanics. Each side views the other with suspicion. That is really a bad thing for our country. This is where I see the major problem with illegal immigration.