$15 was an insufficient placeholder when they first came up with it. It's just the latest in the repeated failure of minimum wage legislation in the USA, which exists to maintain and continue a level of exploitation and human suffering, and enrich the already-wealthy oligarchs of society. It's a position they were forced to accept when their predations went even more unchecked, through the Industrial Revolution, leading to perhaps the greatest mass excesses of mass human exploitation at the society-wide level that the planet has ever seen, anywhere or anywhen.
And I say "society-wide" because I want to carefully distinguish from institutions like slavery (which is part of the discussion, just a separate part from this particular point) where said exploitation was greater, but it was limited to a particular sub group rather than the working class in its entirety.
To bring this back to the minimum-wage discussion, there needs to be two basic concepts established.
1> A minimum living wage. Anything short of this figure means you are arguing for employers to pay staff less than they are worth, less than the basic maintenance of that individual, which thus creates and maintains human suffering as an implicit value that your society supports and maintains, by deliberate design. $15 didn't hit this mark even when it was first being brought up; it's nearly a decade of inflation out of date from where it did originate. That people are so focused on that particular figure is . . . a problem. It isn't a magic number. It's just "better than fucking $7.25".
2> Tie the minimum wage to cost-of-living indices, so that it's automatically updated on at least a yearly basis. That prevents any need to continue making adjusting it for basic inflation a frigging political debate, when it shouldn't be, and the only reason to oppose an inflationary bump on the minimum wage is, again, a desire to foster human suffering so that the wealthy can be even more wealthy than they already are. There is no other reason for doing so. That's it; misanthropic desire to foster human suffering.
I'd go even further and argue that a basic income is an even "better" solution to the same problems, providing that living baseless to all members of society, rather than just workers (and settles all arguments about how many kids and workers should be presumed in establishing what a "living wage" amounts to).
If you're not tying it to cost-of-living and you're not making it a living wage, your position is inherently about creating and/or fostering human suffering for the sake of profit. I understand why the wealthy oligarchs who lack any empathy for their fellow man are against it; naked self-interest is a disgusting motive, but one that's rational if unethical. But anyone who isn't already rich? You're being exploited, too. Not sure why you think your own exploitation and suffering is something to defend and protect. Seems really, really dumb and without any possible explanation that'll hold up to any scrutiny.