The non partisan question is simply, "Who is to blame?"
My take on it:
I believe only the most close minded loyal followers will blame the Democrats.
I think that if the Republican House really does push this all the way that they will lose a lot of Independents and turn off a lot of Conservatives.
You can not be highly visible adding an unrelated item such an anti-immigration to a sensitive and time critical department like DHS, and expect it to be unnoticed or ignored.
If DHS does not get funded it will be blatantly obvious that the blame falls 100% on Republican shoulders.
If Americans die due to a terrorist attack and this happened after DHS has a ripple... there will be hell to pay.