Suggestion 1. It expresses tribal membership: Kevin Drum is fond of this one in other things. In order to win the primary, Republican candidates have to pledge themselves to all sorts of nutty, far-out ideas that would be wildly unpopular (including with most of the Tea Party). The press gives them a free pass on this (Drum complains) because it accepts that they don't actually mean any of that but are just saying it to show proper tribal affiliation and let their fellow Republicans know just how outraged they are that the Democrats are in power.
Suggestion 2. Plausible deniability: I have discussed the distinction between a dog whistle and plausible deniability before. A true dog whistle has one meaning that is open and apparent to the general public and a hidden, covert meaning to insiders. The whole point is for outsiders not to be aware of it. A plausibly deniable remark, on the other hand, is susceptible to two possible meanings, one innocent and one offensive. The offensive meaning is at least as apparent as the innocent one and often more so. The goal is to be called out on the offensive meaning and then become indignant at how the "lamestream media" is persecuting you. In the case of "Second Amendment solutions," the goal is to hint as broadly as possible that you consider armed rebellion a proper response to losing the next election and, if confronted, assure the press that really you consider the need rebellion to be extremely remote and purely hypothetical and that you just keep stressing it as a matter of principle.
Suggestion 3. It pisses off the liberals: Here is the article I recently read that inspired this post by proposing that explanation:
Now this [talk of armed rebellion] is a guaranteed applause line among Con Con audiences, for reasons that have relatively little to do with gun regulation. The idea here is to intimidate liberals, and “looters” and secular socialists, and those people, that there are limits to what the good virtuous folk of the country will put up with in the way of interference with their property rights and their religious convictions and their sense of how the world ought to work. If push comes to shove, they’re heavily armed, and bullets outweigh ballots. It’s a reminder that if politics fails in protecting their very broad notion of their “rights,” then revolutionary violence—which after all, made this great country possible in the first place—is always an option. And if that sounds “anti-democratic,” well, as the John Birch Society has always maintained, this is a Republic, not a democracy.In other words, liberals tend to resent being told that armed rebellion might be justified if they win the next election. Right wing politicians have noticed this and therefore trot out the threat of armed rebellion as an applause line, not actually meaning it, because it pisses off liberals. It is, after all, part of a longstanding tradition on the right to spew a lot of outrageous talk with the clear but unspoken understanding between speaker and audience that such talk is pure theater and not to be taken seriously. The main purpose is to give offense.