The problem is, most of what you have written is not true. Illegal aliens have jobs, homes, drive cars, and receive government support in some degree or another.
The real problem is in a broad sense, illegal aliens are people who failed to figure out how to survive in the failed country of their origin. Other than what appears to have been a desire to work, there is little else they have brought with them.
Many of the challenges related to income, government deficits, lowered tax revenue, and challenged education systems can be directly attributed to this massive influx of unskilled, and poorly educated people.
The attaction of a relative comfortable life must be removed, and the real consequences of their illegal entry enforced if these problems are ever to be addressed.
A sane guest worker program is needed, and severe penalties for breaching our immigration laws must be enforced.