The fallacy is that it's worth taking guns away from hundreds of millions of law abiding citizens to save a few lives. If that's the logic, then why not look at saving lives where you can do it in much bigger numbers?
Edit: Working on a TL;DR. Please stand by heh
1. Most here don't advocate complete gun removal, so the premise is a straw man argument.
2. Slippery slope argument of the gun lobby et al is just that. It is not possible to get rid of all guns and it is not desirable by most reasonable people.
3. We can agree that the process of determining who should not be able to buy a gun has issues, that is something we must debate for good reason.
4. We can strike a balance between the various freedoms and the greater good without ruining the whole or any one freedom or liberty.
5. Personal autonomy ie cars and such are essentially rights in a modern society and can't be done away with nor should they. Infringing on driving affects more people in a real way than gun control is ever likely to affect the same number of people or as dramatically.
6. Cars are made safer as a matter of course. Guns are made more dangerous as a matter of design and purpose. In addition gun culture wants guns to push the limits as dangerous as the society can accept.
7. Cars and guns are both potentially deadly. So both need to be addressed. Cars are constantly being improved with safety technology, while guns are meant to kill and their safe usage as far as accidents are concerned is an intractable problem.
8. NRA/gun industry has the strategy of not giving an inch on any aspect of loss of gun freedoms as they see it. This trickles down to gun owners such that they mirror their leadership thus having a reasonable discussion of improving gun safety much more difficult than car safety.
Conclusion, cars are essentially a right, even if not defined as such and even if they were a right they should be regulated for safety and they are. Guns are a right and will not be done away with, should be regulated for safety and they are. Both can be improved, but one embraces safety and the other resists it.
The "meat" follows

insomniacs, you can thank me after you wake up, you're welcome!
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Those of us here seem to be talking about common sense laws about gun safety and not about the wholesale removal of all guns from our citizens. Some of us own guns and all of us appear to think the 2nd amendment is worthwhile. Its interpretation is debatable obviously and how it should be implemented is debatable, but I think you will find us here not looking to dismantle and smelt every gun in America.
So, the hyperbole of the premise you allege we stand for of taking away the guns of hundreds of millions to save a few lives is the fallacy. Our position is that our agencies must do a better job with enforcing the safety laws already in place and try to do reasonable things to keep guns out of the hands of those that demonstrate they are a risk. Admittedly that is imperfect and some law abiding citizens will be at best inconvenienced or at worst will have a right infringed, but the alternative of allowing every citizen no matter their past or potential the easy access to a gun in the name of standing up for the amendment is foolhardy and extreme. I am sure no reasonable person feels that way, so I won't take my rhetoric in that direction in my arguments. The reasonable happy medium between no restrictions and full restriction is always going to be closer to the gun ownership side for no other reason than the difficulty of getting a big change through our government. Changing the constitution? Forget about that. That slippery slope argument is unrealistic and used to get the base riled up.
Some number of citizens, not in the millions, that are being watched or have some red flag will be the ones that get trampled on. We can agree that there will be those that don't deserve to be on that list and that is unfortunate and very wrong. We should have methods in place to correct errors and remove false positives. I assume that you feel as I do that this is not their priority and for them it is better to cast the net wide and worry about removing the dolphins from the tuna net after all the tuna have been caught, as in never. But since we are already infringing on the rights of suspected terrorists by having no fly and personal information collected, what is it about them not having a gun that is so problematic? There will be enough patriots with guns to serve in the militia! Anyway, that point of how we determine who should be unable to acquire guns can and really should be discussed.
The intersection of liberties and peaceful coexistence are at odds at times. Sometimes one trumps the other, but if we strike a reasonable balance we really can do what is right for the greater good.
Part 2
Personal autonomy is something everyone can identify with as opposed to bearing arms. Whether it's driving to get your groceries or buying unhealthy food once you get there. We can all agree that the choices we make about our freedom to move about and how we take care of our bodies is fundamental to our very existence. So, if society wants to make inroads on preventing death from transportation it has factor in what freedoms would have to be lost. What economic losses would be incurred. And how would society function without personal transportation as it exists today?
Automobiles are, in general, safer today than 40 years ago. The direction most humans want from their transportation is to get safer and safer since it is a potentially dangerous activity we must engage in nearly every day for sometimes many hours a day. The manufacturers are aware of this economic incentive and additionally are forced by regulation to do things to continually improve safety.
On the other hand when it comes to guns, while there are naturally those that are very strong advocates for gun safety, there is a desire by the NRA and some gun advocates that if you give an inch on changing any regulations about guns you will eventually embolden the gun control side to keep stripping away at guns until guns are either emasculated or removed from circulation. This natural propensity for such a powerful leader of the gun industry to shape gun owners in to a confrontational us vs them stance goes against reasonable discourse and proper decision making. The NRA is about the NRA and not about what is safe for the population as a whole.
Cars aren't going away, guns aren't going away. So the question is how can you improve the safety of both? It isn't a zero sum game. Cars kill more because it is a part of daily existence and nearly unavoidable. Guns kill fewer people because they are not a daily hazard that must be navigated. So just because one kills more than the other doesn't mean we can divert attention from one to another. Car safety is being addressed to a balanced degree as technology and other pressures advance, and gun safety makes no significant advances and is actively being fought against to different degrees.
There is an incentive to make daily transportation safer. There is an active disregard for having a safer less deadly personal firearm. By its nature you want it to be deadly. And for many, it seems, the deadlier the better. In addition, the gun culture/lobby/industry wants to push as far and as hard as possible in the direction away from infringement on gun control and regulation in order to keep the flag in the middle of the tug-of-war on their side as long as possible. If you lose an inch you may never get it back.
I apologize for the lack of editing, I saw some repetition of points, but I hope you won't throw me out of bed because of it. More importantly I hope my arguments are not full of shit. Please correct me where I am using faulty reasoning.
Thanks if you made it this far