I'm going to presume we're talking about an outright ban with confiscation and no grandfathering. Reaction would certainly be much more extreme with certain classes of firearms, and I'll further presume we're not talking about ALL guns. Not even in the UK have they tried that, yet.
Interesting question. As I think about it, I foresee a couple of different possibilities.
1) Much like in Canada, the UK, Australia, D.C. and New Orleans, the people would complain but comply. I have no doubt this and nothing more would happen in some regions.
2) An avalanche of lawsuits would reign down. This most assuredly would happen, and I have no doubt--whether against an outright ban on handguns, ugly guns, or all guns. The NRA and SAF sued to stop Prop H in San Francisco. Sheriffs Printz and Mack filed suit in response to the Brady Law. No one would sit still for this.
I don't believe our side would give in before the matter came before the SCOTUS. I mean we'd have nothing to lose.
Perhaps the antis would give up after losing at the Circuit Level. However, I suspect if they had the momentum to get 51 Senators (perhaps 60) and 218 CongressCritters to vote Aye on such a measure, then they would not allow that momentum to die before the matter came before the SCOTUS.
In either event, an outright ban on everything would be overturned by today's SCOTUS and would fail on a vote of between 7-2 and 9-0. A focused ban on one class of guns--be they handguns or ugly guns--would fail on a vote of between 5-4 and 7-2. One or two of the Justices might overturn an outright ban, not on Constitutional or legal grounds, but to prevent a Civil War. No one wants to be the guy remembered for triggering The Second Civil War.
3) I would like to believe the lawsuits would quickly come before the courts and be stayed before ANY action could occur. However, there's a chance some confiscation could begin--perhaps under the auspices of "early voluntary compliance". If confiscations did begin, Feds and locals alike would be involved. National Guard? Maybe. Regular Army? Doubtful. This leads into #4.
4) Resistance. Even against the Borg, it is NOT futile. Some would successfully organize peaceful non-cooperation. The NRA, SAF, CCRKBA and GOA would probably organize most of it. Sane people don't want civil war, but sane gunowners would choose it over disarmament. Sane leaders know that if a ban could be stayed long enough to get before the SCOTUS, it would die a death that would cripple the antigunners with Supreme Court precedent. With that precedent, bans in D.C., Chicago, et al. would be gone. The '68 and '34 bans and restrictions would also probably be gone. In the aftermath of the '94 ugly gun ban, it has been largely downhill for the antigunners over the past 12 years. The legislative reprecussions after an outright ban and confiscation attempt would be severe. It would be darned near pre-1934.
I believe that even in the face of an impending ban, gunowners would be very willing to try a peaceful solution. 10,000 gunowners descending on Washington, D.C. could effectively shut down most federal LEAs with a sea of bodies blockading the front doors. The same in each of the 10 or 20 largest cities could be economically devastating, and a lot of fencesitters as well as antigunners know it. The fencesitters would begin saying "This ain't worth it. Let 'em keep their danged guns. Crime rates are down anyway. Maybe some other time."
5) Civil War. I provided no interrim of violent resistance following peaceful resistance as I don't believe there would be one. I think once the shooting begins, that's it and we're in for a bloody, brutal, violent war that will make the Nineteenth Century Civil War seem like a minor skirmish. When it all ends, however it ends, there will be millions dead. Greybeard7 mentioned "Unintended Consequences", but I don't foresee it being that clean or organized. There will be violence between different racial groups that has absolutely nothing to do with the Second Amendment or the gun ban. It will be bad.