You think this prevents criminals from getting guns? Really?
But look at it another way. If something is a "right" they why do you have to ask permission to exercise it? The egregious Brady law forces up to ask the government's permission to exercise a right. Hence it is no longer a right, but a privilege. So with the passage of the instant background check, the right to purchase firearms went away to be replaced by the privilige to purchase firearms at the government's discretion.
The FFL is licensed under the Commerce Clause, because they're involved in an interstate market. The instant background check applies to any transaction they wish to make. The intent of the background check is to make sure they do not sell to prohibited persons, because they have forfeited their right as I explained above. Even the FFL is not obtaining permission, it's a requirement. The result of the background check just says there are no records that disqualify the buyer, or their are.
The background check does not amount to the buyer having to ask permission. The buyer only has to provide his name and fill out a form, which asks questions regarding the disqualifies. That does not infringe on their right to keep and bear arms. The disqualifies have a potential to do that, such as Lautenberg, but most of the others don't. So, it's the disqualifiers that may infringe on the right, not the check itself.
"You think this prevents criminals from getting guns? Really?"
It prevents them from engaging in the legal market. That is good enough. There's no logical reason to allow a freshly released thug, or psycho to walk out of a gun store with a smile on their face. Let them walk out with a frown mummbling to themslves.