"I'm all in favor of the idea. The only thing that bothers me is that the term "march for justice" has more of a liberal connotation. If we can call the effort by some other name or slogan, I think it will be more clear to more people what this is all about."
The cry for "Justice" is not exclusively owned by "liberal" tyrants, like the ACLU, who are really leftists operating under "democratic" fronts. "Justice" is an American connotation. There is nothing "just" about leftist' mandates to over-power and deconstruct America.
If the main purpose of the march is to get our judges or justices a fair vote in the Senate, then indeed call it by what it is: "March for Judges."
It is not a concession to leftists if you don't call your causes by the same name as they call theirs. It will only confuse people. And people is what you want to attract.
Drive by a billboard that reads "March for justice" and it immediately evokes the image of Sharpton spewing his nonsense. "March for Judges" is sraightforward and conveys the message you're trying to deliver.