In principle I think there are few reasons to oppose a background check.
Calling it "the gun show loophole" is a propaganda term that doesn't represent the reality.
I have attempted to purchase firearms at a gun show. Once many many years ago when my driver's license was expired and I was turned away at Doug's Shoot 'n Sport (local gun shop that's been around for a long time) I tried to get a gun at a gun show. It didn't work. Wanna know why? Because all the people running booths at the gun show were gun store owners. Because they had a Federal Firearm Licence (FFL) they were required to run the same background check as they would have in their store. So, while it would have been possible for a private citizen to rent a booth at the gun show and sell guns from his/her private collection and not run background checks I haven't ever seen that.
I'd like to see someone go in with a hidden camera and try to buy a gun at a gun show without doing a background check. I bet they'll leave empty handed.
The "loophole" that is actually being closed is private person to person firearms transfers. So not only will I have to perform a background check if I want to sell a gun on craigslist, but if my uncle wanted to return some guns that used to belong to my father we'd have to run a background check.
So, how would this work? I can't run a background check from my computer or smartphone. So all private sales would have to include an established FFL holder as middleman so that they could conduct the background check. There is currently a standard practice where a gun store will receive privately ordered firearms from out of state because guns cannot be shipped except from FFL holder to FFL holder. Then you go to the gun store pay a fee, usually around $25 but I've seen as low as $15 and as high as $40, plus the cost of the background check that they're required to run before releasing the gun to you. So in the case of my uncle wanting to give me guns that used to belong to my father to do it legally we'd have to meetup at the gun store, pay the fees and then he could give me the guns.
That's the goal of closing the "loophole." To make private sales of guns get a background check. gun shows have almost nothing to do with it. The gunshow loophole was a fake problem that happened to get a lot of people riled up so they've been runnin' with it.