Sure but keep in mind that most of these people pay taxes into a system that they don't actually benefit from (social security for one), so by doing so you're actually causing more economic damage than you think you're fixing.
So if someone lives here, works and pays taxes, and has not been convicted of any other crime... why would we want to deport them? By some measures migrants pay more taxes and commit less crime than natural born citizens. We should just get them paperwork and let them continue being good citizens while we also reform the process that resulted in them being here illegally in the first place.
Why should we spend billions of dollars on this problem that in many ways, on paper, is beneficial?