No, its not. Its a problem for progressives. But mostly that's because, in the US, progressives are stuck (to have any meaningful impact at all) in a big-tent party with liberals, who actually oppose most progressive policy goals and methods, and align with conservatives in undermining them most of the time, except when they decide to tolerate them to get support for a liberal goal against conservative opposition.
It's a fairly big practical difference between the right-to-further-right coalition in the GOP vs. the center-right-to-center-left coalition in the Democratic Party that the main factional differences in the former coalition are matters of degree and those in the latter are of opposing ideological principles.
Because it has nothing to do with slogans themselves. It has to do with double standards whereas whatever conservatives do is always interpreted in the most favorable way and what libs do in the least favorable way.
They've had their moments too. "Read my lips: no new taxes","Whip inflation now","Lock Her Up","Strong and stable","In your heart, you know he's right", "Drill, baby, drill"
It's a constant problem for libs. What's the last liberal slogan you can remember that was catchy and that didn't completely backfire or get twisted?
That doesn't happen to conservative slogans.
I don't have a dog in that fight. I'm just an observer. It's "funny" like a dad joke to me by now, though.