How large? I’ve seen multiple definitions of political independent, with varying sizes as a proportion of the electorate.
One definition is “people who are registered independent.” While this is an easy way to differentiate, it does have an issue that many of them are in fact less than independent in terms of their preferences. Gallup categorizes independents as “Lean Republican”, “Lean Democrat” and “non-leaning” independents. In one of their polls from last year, published early this year, 47% of all voters were Democratic or leaned that way, and 42% were Republican or Republican-leaning. This left only 10% of the electorate (not up to 100% because of rounding) that were considered true independents.
You probably can’t pick up a whole lot of the other side’s leaners. Some, perhaps, but some of them are declared independents because of their disgust with their party, often because they feel the party hasn’t gone far enough towards their preferences. In other words, identification as independent doesn’t necessarily correlate with political moderation ideologically.
So how do you activate the true independents? Some of them will be too caught up in their own “a pox on both houses” rhetoric to do much of anything. There’s no indication of any kind of consistent political or ideological thought involved among those independents - indeed, the president’s baldfaced lying probably ended up appealing to some in this category simply by virtue of their picking and choosing what to pay attention to and what to disregard, along with the Republican party and its associated political machinery slicing-and-dicing the electorate, microtargeting voters with precision that it seems like the Democratic party doesn’t do well (of course, with Zuck, Musk and the like going all MAGA, who could trust them to help?)
Will independents help you in the off-year elections? Perhaps, but it’s usually harder to motivate low-propensity voters when the President isn’t at the top of the ballot. Of course, when the margins are this small, you don’t want to alienate anyone you don’t have to, but you might lose as many on your extreme flank as you do from the middle.
It’s tough. The modern electorate is near-evenly split, and - in part because of that - highly inconsistent. I do think that in times such as these it’s more important to stand on principle than to sell out temporarily for power, but that’s a hard stance to take when the consequences of an electoral loss are so huge.