I'd be in favor of this -- as for the gov't "knowing" -- there are somewhere between 200 million and 400 million firearms in the USA. If Obama declares himself President For Life, he can just start a house-to-house search at #1 on any street and keep going. In 1000 years, they might manage to find a lot of them.
The number of guns stolen annually is estimated at about 225,000 in the WSJ article linked below, although I have seen much higher estimates. It would be nice to see that figure reduced, but I admit that involving the Fed has a number of drawbacks.
Here's a stat from the WSJ article that troubles me: in 1993, 54% of households said they owned guns, while that figure is only 41% as of 2010. Urban dwellers, immigrants, liberals coming of age and starting their own families, etc. are part of that erosion. I'd love to see any policies that could be a part of reversing that trend.