A lot of slogans (and this goes for advertising as well as politics, since slogans are a sort of political advertisement after all) follow one of the following patterns:
Three words are optimal in many languages. This was quite explicitly stated by Nazi propagandists (Goebbels made it an explicit rule), but has also been found whether consciously or unconsciously by propagandists of all ideologies:
Bomben auf Engeland!
Dieu le veut!
Вся власть – Советам!
Black is Beautiful!
Drill, baby, drill!
Éirinn go Brách!
Alba gu bràth!
Liberté, Égalité, Fraternité!
Tiocfaidh ár lá!
It's interesting in a way that those of the above which aren't English but which remain in three words in translation ("Bombs on England", "God wills it", and "Liberty, Equality, Brotherhood") retain the most force while those that don't ("All power to the Soviets", "Ireland forever", "Scotland forever", "Our day will come") lose some of their impact. Indeed, Dieu le veut was first found as the Latin Deus vult, but the French packs more of a punch.
They are easily chanted, work well typographically, and are a microscopic example of the Rule of Three, and just long enough to convey an idea without being long enough to encourage people to think about it too much.
Longer slogans tend to turn on a conjunction or a copula between two roughly equal-length parts:
Come and take it!
Give me liberty or give me death!
Each for all and all for each!
The personal is political!
The rich get richer and the poor get poorer!
Vivre Libre ou Mourir!
Adam and Eve, not Adam and Steve! (comma rather than conjunction, but similar pattern)
In visual use, instead of a copula there could even be an equal sign, as in the ACT UP slogan:
Silence = Death
Anything longer, if spoken, than that will generally rhyme and have a balanced rhythm:
Keep your rosaries / Of our ovaries.
We are gay, we are straight / It's the bigots that we hate.
Hey, hey, LBJ! / How many kids did you kill today?
One, two, three, four / We don't want your bloody war!
One, two, three, four / Fuck the rich, feed the poor!
Six, seven, nine, four, seven, double-oh / A woman has the right to know.
Vårat svar på monarkin / gör som Frankrike, giljotin!
These last though are more appropriate for several rounds of repetition.
Anything longer than that or without a rhyme, tends to work better on a placard than spoken, and then things are a lot looser. Snappiness and two-part balance still often feature.