[Wonder Warthog]

"Treaties go through the Senate. They have nothing to do with the House."

True. But any funds for enforcement have to originate in the House. But it would be preferable to get/keep enough pro-gun Senators to block action there as well.

[ConjunctionJunction]

Yes, the key would be in stopping the treaty in the first place. Otherwise, the House will cut funding about as well as they have with Obamacare.