I was on the hill when the initial congressional negotiations over immigration began in the mid-2010s.
The stumbling block has always been illegal immigration. [0]
The Dems congressional leadership at the time decided that no reform on legal immigration would happen without illegal immigration reform (eg. DREAM act)
The GOP congressional leadership at the time decided that no reform on illegal immigration would happen without legal immigration.
Neither side budged, and neither side really cared because immigrants (legal or illegal) can't vote.
[0] - https://www.politico.com/story/2013/12/nancy-pelosi-immigrat...