It was mostly Republicans who killed comprehensive immigration reform in 2007; it was overwhelmingly Republicans who killed the DREAM Act in 2010; it was even more overwhelmingly Republicans who killed comprehensive immigration reform in 2013. It was a Republican president who canceled DACA in 2017, and it is exclusively Republicans who are blocking a wise and humane legislative replacement for DACA in 2018.
The real reason Schumer and Senate Democrats are struggling to secure help for DREAMers is that there are only 49 of them in a 100-person body (and you need 60 to pass legislation), their colleagues in the House are even more disempowered than they are, and the executive branch is controlled by people who are fundamentally hostile to the cause.