If someone is pushing the "gun show" thing, they are showing you their lack of understanding of the issue. I would be interested in knowing if the New York Times is pushing the gun show sales as a problem.
There is no "gun show loop hole." Every retailer which sells at a gun show must run background checks as if his customers were in his store.
The only gun transactions which do not require background checks are private transactions, such as me giving a gun to my son whether as a gift or inheritance, or a friend selling a gun to a friend.
You would have to support making private transactions illegal unless they are through a licensed gun dealer, which costs money (usually 10% or more of the value of the gun). The dealer would run the background check. Or, make the federal background system available to private citizens. But, it doesn't matter, because criminals would just ignore this rule anyway.