There are at least two major reasons why some people would oppose the sort of comprehensive immigration reform that President Obama spoke of recently. One of these reasons is pragmatic while the other is more idealistic.
On the pragmatic or practical level, there are people who will oppose this because they believe that it will make life harder for American citizens. Under these comprehensive reforms, millions of people who are currently here illegally might become legal. If these people were expelled from the country the way many want, there would arguably be more jobs available for Americans with less education and fewer skills. Therefore, reform would harm those people while a tougher stance would help them by opening up jobs.
On the idealistic level, there is the idea that these reforms are in essence an amnesty for people who have broken the law. People who hold this belief argue that all illegal immigrants are criminals. They have all chosen to act in ways that were clearly illegal. If our government were to allow these people to become citizens, it would be rewarding them for their illegal actions. Regardless of the consequences, they say, this would simply be wrong.