This whole issue becomes easier to understand if we put a few things in perspective first. First and foremost, it must be understood that under our current laws, any time a prohibited person acquires a firearm, at least one person has already comitted a crime. Not only is it illegal for a prohibited person to acquire a firearm under any circumstance, but it's also illegal for someone to knowingly supply a firearm to someone that they have reason to belive is a prohibited person.
Secondly, private party sales are but one means for a prohibited person to acquire a firearm and I've yet to see any evidence that it's the most prevalent, or even a particularly common, means. Theft and straw purchases are other means which come readily to mind. Since acquiring a firearm by any means is illegal for a prohibited person, why should we think that one would care which law they're breaking?
Third, the government has given us no reason to believe that they would enforce a law requiring universal background checks any more effectively than they've enforced the existing gun laws. If you are a prohibited person, you cannot fill out the 4473 truthfully and still appear able to purchase a firearm. I have to wonder how many prohibited people have turned to other means like theft, straw purchase, or private-party sales only after being denied on a NICS check. Perhaps if we prosecuted more of the people who lie on the 4473, posession of firearms by prohibited people would be less of an issue.
Finally, the only way to make Universal Background Checks even remotely enforceable would be through registration and even that could be circumvented by a clever enough person. There are currently between 390 and 465 Million privately owned guns in this country and they will likely remain in circulation for decades. Without registration, all a person would need to do in order to avoid prosecution for an illegal private sale is claim that the sale took place prior to the law's enaction. If anyone thinks for a moment that, without a registration requirement, the anti's will ever admit that Universal Background Checks simply don't work, then that person hasn't been paying much attention to the anti's playbook. Instead, they'll blame the failure of UBC's on the lack of registration and push for it later.
Even with registration, the law could be circumvented by the seller simply reporting the gun stolen. Since posession of an unregistered gun would already be a crime, why should the buyer care whether the seller reports the gun stolen or not since he's already in posession of illegal goods?
Registration is an extremely poor idea for a number of reasons. First, it allows for easier intimidation of lawful gun owners such as we recently saw with The Journal News in New York. Such an abuse would never have been able to happen without NY's registration requirement.
Secondly, it facilitates confiscation of lawfully owned weapons by over-zealous officials during a state of emergency such as we saw in New Orleans after Hurricane Katrina. While such confiscation may be illegal, it would have to be overturned throught he courts later and that would be of little help to the people who need their firearms then and there.
Finally, and most insidiously, it opens the door to selective enforcement and abuses of power by corrupt officials. Anyone who believes that officials in all levels of government could be trusted not to selectively enforce such laws only when politically convenient and only against those whom it is convenient for them to prosecute is deluding themselves. Without getting too political, the precedent has already been set by the executive branch of our government that enforcing laws which are deemed not to be politically expedient is optional. Why should we believe that gun laws would be treated any differently than the other laws which are selectively enforced?
So, when everything is considered, I can only come to the conclusion that Universal Background Checks, through an attempt to ban activities that are already illegal, would only place undue burden on law-abiding gun owners. Going the asinine route of making gun crimes "double illegal" isn't going to phase a criminal who, by definition, does not respect the law. The way to stop criminals from committing crimes is not to pile on more redundant and unenforceable laws, but to punish them for the crimes they've already committed. Personally, I think that if someone represents such a danger to society that they cannot be trusted to own a gun, then that person should remain locked away from society until they are no longer a danger. Violent criminals need to either remain incarcerated or, if the crime is severe enough, be executed and the violently mentally ill need to remain institutionalized until they can be treated to the point of no longer being dangerous.