Some American politicians have hinted at the possibility of mass amnesty for illegal immigrants, but it is an issue that is widely unpopular--partially due to how that could change the eligible voter population.
I think it is more likely that amnesty either never happens, or it is only offered to specific small groups of people.
Otherwise, America is extremely unkind towards anybody who breaks their laws--especially if your goal is to later apply for a visa or Green Card.
Finally, crossing through the southern border is not so easy. Other immigrants die when they make the journey.