In the spirit of the OP I'll try to keep it to "if" not "whether" guns are banned.
First, my personal take is that if it happens in the next ten years there will be no initial attempt to make it an uncompensated seizure. They couldn't cross that hurdle in Britain or Australia and we've got the fifth amendment that would have to be jumped in addition to the second. Besides, there's a lot more of us.
If our politicians take a cue from our Northern neighbors the cost will be presented massively understated.
It's pretty easy to estimate a cost: it's around 1,000.00 per firearm assuming no inflation, a 100% voluntary compliance rate and minimal infrastructure and bureaucracy. See:
Assuming 70 million handguns and 30 million semi-auto shotguns, rifles and what-all, the lowest possible monetary cost is 100 billion. Again, using the Canadian experience, we can estimate the actual cost to be a minimum of ten times that or a trillion dollars.
A bunch of folks approaching retirement will be all over it – cash up front for something we weren't sure we were going to sell and we've still got all our Fudd stuff. Of course there will be a tsunami of claims filed contesting the amount of compensation. The claims are a full three orders of magnitude more than the British experience prepared anyone for. The legal system grinds to a halt.
That should have the compensation cost of 100 billion pretty much torched at that point – the electorate was aware of the 100 billion, this is where they learn it only primed the pump. First, they'll have to swallow the relatively bitter pill that they’re going to have to raid the Medicare levy. It's not like it hasn't happened before:
But, as they say: "In for a dime, in for a dollar". Around 20% of banned firearms are in and the cost is sailing past the 100 billion mark like it was tied to a post. Now we start printing money. Unlike the Wall Street bailout where there's at least something for the money, the 100 billion has been spent on flame cutters and furnaces – they're literally burning wealth. The impossible has been achieved: they have worked out a way of assuring less return on taxpayer money than the bail out.
About 400 billion into it somebody finally floats the idea of no compensation. It can't be cut out altogether but it's reduced sufficiently that non-compliance spikes and stays spiked.
Some genius in congress finally notices that Britain's handgun surrender was performed with, at maximum, 1/3 of 1 percent of the population owning handguns (162,000 handguns with a general population of 50 million) and it just doesn't translate into 20% of the population owning banned items. His intern notices that Tamara said as much on page 3 of a thread dating from 2008.
162,000 != 100,000,000. Only a very special few could believe that it is.
But it's too late. The USA now aspires to be a third world nation having spent all its wealth on stuff it destroyed. Those that received payment find that it's not worth the paper it's printed on.