First, this isn't exactly 'news'. Not only did we know it was coming this time, but Carolyn McCarthy has introduced the exact same bill at the beginning of Congress, every single year.
In this case, this is basically going to be the house version of Feinstein's bill. Of course this one seems more 'reasonable' with only a high-cap ban.
Now, I'm not a political analyst, I don't know all the ins and outs, but it SEEMS to me, Boehner can do a couple things here.
First, he can refuse to let it go to a floor vote. This will probably have some severe backlash.
Second, I believe he can merge this with the Feinstein bill. The Feinstein bill is basically a giant self-made poison pill that has an unlikely enough time in the Senate, let alone in the House. This will probably kill both of them dead.
Of course, these are just OPTIONS he has. He's a Representative, so we have to TELL HIM THAT WE DON'T WANT THESE BILLS.
THEN he, and the rest of the Representatives can kill it for us.