Sure, as long as the new immigration laws don't include giving amnesty to illegal alien lawbreakers. If they do, Americans will protest against those laws, like they do against any law they dislike or that they feel is unfair, unethical, or immoral in some way.
Now you're crawfishing. If the only thing you say that counts is whether they are legal then you have to like them whether they became legal by reason of amnesty or otherwise.
The fact is that the antis will never support a new law that allows for the same number of immigrant laborers. What they have always really wanted is 9 million Mexican laborers kicked out and none allowed to return.