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As usual, and right on cue, the Republicans' messaging on this whole episode has been horrific.
They could have responded to this in two ways:
1. By calmly explaining and reinforcing their desire to enforce existing law, ultimately deporting anyone who is here illegally and indirectly causing them to "self deport".
2. By screaming "AAAUUUGHHH! He's a Marxist! He's a dictator! He can't do that! AAAUUUGHHHH! That's unconstitutional! He's an emperor! AUUUUUGHHHH!"
Which route do you s'pose they chose?
Maybe they know that the first option would be a lousy political move and have decided to just go postal, who knows.
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And yet the far left wants to make new laws that will not be enforced.
The Republican House tried to do this earlier in 2014, for the DACA program, passing a bill that would have prevented anyone new from signing up, and preventing current beneficiaries from renewing. Democrats controlled the Senate, so it didn't come to the floor there. Once Republicans take control of the Senate in the New Year, they could pass a similar bill — but Obama would almost certainly veto it.
Rather than a standalone bill, Congress could attach riders killing Obama's immigration programs to the annual appropriations bills. If Obama vetoed the bills (or if Senate Democrats filibustered them) then we'll have another government shutdown.