Boehner won't put it up for a vote. He knows that a Republican White House can just write an executive order rolling back the Obama executive orders and mitigate the damage. The proposed Obama executive order, IIRC, doesn't confer citizenship on the illegal immigrants. A Republican President can probably figure out how to roll back quietly the executive orders. Far better, in short, to ride out the storm of the next two years, convene with Republicans in control of both chambers of Congress, end the filibuster, roll back the executive orders, and pass whatever they want.
It's not the first time this has been done. Bush rolled back Clinton's last minute executive orders. This is in other words not a fight worth picking.
Nobody will be impeached. There's a White House to be won, and the stakes in 2016 are too high for the GOP to play this kind of chicken crap. This isn't 1998 either.
I can't imagine a 2016 campaign where the Democratic candidate doesn't make hay of the fact that a Republican candidate would roll back the EOs, quietly or not.
