Amnesty is defined as "an official pardon for people who have been convicted of political offenses". One of the bills that includes funding for the "wall" and other stuff trump asked, plus a path to citizenship within 10 years is something doable. Adding another 3+ million plus parents and relatives will not do well in the house.
Waiting 10+ years to become citizens is not Amnesty. I think the hardliners want to make sure only DACA eligible people benefit from this and not open the door to more people.