Not One Dime! No More Wars! Save Our World! We Want Jobs! Count Our Votes!
Any other suggestions?
A couple things here.
1) I think you're getting too caught up in Trump's rally chants. By repeatable and simple I'm not talking about something that necessarily has to be chantable, and in fact, I think getting too caught up in crafting "something your supporters can chant" heavily limits the options of what you can lead with as a party. "Neatly conforms to a 3-syllable slogan we can recite in sing-song" shouldn't be a driving criterion for platforming. My point rather was that the platform positions should be things that can be expressed succinctly and coherently in such a way that: a) everyone knows exactly what the position represents, and b) anybody can repeat to friends, family, or even strangers on the street. "Build the wall," happens to conform itself well to chanting, but more importantly represents a clear agenda centered around a simple call to action which anybody can internalize and repeat to others as a way to win over allies. The distinction isn't between "build the wall" and "build the effing wall" (i.e. chantability) but "build the wall" vs "We should implement a comprehensive scheme of border security comprising an expansion of ICE, restriction of visas, and the extension and fortification of existing border structures" or "We should build a border perimeter consisting of a fence of metal slats roughly 30 feet in height with deep concrete foundations so as to prevent tunneling." Obama's "Change" is a good example of what I'm talking about. It's a simple message which points to a larger ideological framework that is immediately understandable to anybody you tell it to and which supporters can easily use as a tool to proselytize. It also makes it easier to jam the airwaves with your message. While your political opponent is busy trying to pick apart the dangers of such a vague slogan, you've already told 10 more people about "Change." This was very visible in 2016: A Democrat may be able to spend 5 minutes explaining cogently why the construction of a wall is financially, logistically, ecologically and geographically absurd and pointless, but by that point the potential Trump supporter has already tuned out and went to tell his friends about the Wall. "New Deal" is another great example of an extremely simple and effective political slogan.
2) I think a big component of whatever message the Democrats choose for 2020 is that it has to be 1) a concrete policy, 2) a positive call to action, and 3) representing a general issue (i.e. not a response to a specific event). On the basis of these three criteria, I don't think any of your proposed slogans really work.
Here's the why for each one:
Not One Dime! - it's a good slogan in this moment to rally the Democrats as a coherent front to petition congress not to cave to Trump's demands. But as a slogan for 2020, it is at once too specific and too vague. It is too vague in the sense that, absent the context of this budget fight, it is completely meaningless. Not One Dime - whose dime? why? for what budgetary issue? Either the slogan directly refers to this budget fight which will be a nonissue by 2020 and many voters may well have forgotten about it by then, or it's intended as a general national condition, in which case it means nothing. It also fails on the point of representing a positive call to action. It isn't positive, i.e. it isn't saying what you
will do when elected, but rather what you
won't, and it isn't a positive action in that it doesn't command the voters together to
do something. All this slogan does is place your party within the context of the other side, which you don't want to do because 1) you're essentially giving the Republicans free messaging (Not One Dime more? For what? The Wall. Oh yeah! Build the Wall!), and 2) it runs into the thing I mentioned before, dispositive messaging requires you to build a case for why you won't do
the thing, and in the time you've spent building that case, the other side has told hundreds of other people about
the thing that they want to do. Plus the slogan is really bad optically: "Vote for us so we can go to Washington and not do stuff!" If the objective is to message about border security or immigration reform, you should slogan around those positive, actionable issues. "Citizenship for DREAMers" or "Path to Citizenship" or the like.
No More Wars! - Again, it's not positive, and not actionable. It's not good optics to campaign on what you
won't do. It's not exciting, it doesn't capture the popular imagination. "Vote for us so we can go to Washington and not do stuff!" If the slogan is about ending our military presence in Syria/Afghanistan/Iraq it should be "Bring Our Troops Home" or something like that. If it's about reducing the military budget, the slogan should say something about that.
Save Our World - Too vague, and it doesn't represent a clear call to action. It sounds like a plea. Either the politician says it and it comes across like the politician doesn't have a plan and is asking for someone else to do the job, or the voters say it and it makes the voters sound powerless - it sounds like a plea for help. This is an example of what I was referring to when I said that hyperfocusing on chants ends up weakening the overall message. "Let's save our world" sounds much more powerful, although, again, it doesn't refer to specific policy proposals. Green New Deal has the advantage of conveying a straightforward message that is understood as "saving our world" and representing concrete, actionable policy proposals. "Send us to Washington so we can implement these specific policies that our nation desperately needs"
We Want Jobs - Similar problems to "Save Our World." Either the candidate says it and it sounds like the candidate doesn't have any idea of what to do, or the voters say it and it deprives them of agency. It also looks bad optically, "Look at these entitled Democrats demanding a handout!"
Count Our Votes is a good one, although again I'd prefer it to center around a specific policy to implement.