http://en.wikipedia.org/wiki/Snake_Goddess#Interpretations is the source for the two exposed breast premise.
I'll let someone who knows more about either subject--modern democratic symbolism or Greek symbolism--but I can tell you that the Snake Goddess you're citing is Minoan, from the island of Crete. The connection between Minoan culture and religion, and classical Greek society and religion, is often unclear. The most famous example is Linear A and Linear B. Linear B has been deciphered and is an early form of Mycenaean Greek. Linear A is older and uses similar looking letters, but is more often found at insular sites and is still undeciphered (ciphered?). Likewise, the statue that you're looking at is Minoan, and the connection between the figure she represents and anything from classical Greece is unclear (though widely argued). But just keep in mind how separate the figure is from classical Greece as well. The figures are from ~1600BCE. Classical Greece was the 5th and 4th centuries BCE (roughly ~510 BCE to the death of Alexander the Great in 323 BCE). Archaic Greece, the period before the Classical one, is ~800 BCE to ~500BCE. These figures are even 800 years before the thing that comes before what we think of when we think of "Greece".
The "breasts exposed-->mourning" is something in Homer. But as far as I know, it's only in one scene, where Hecuba is mourning her son Hector.
the old man spoke,
his hands tugged his grey hair and pulled it from his head.
But he could not sway Hector’s heart. Beside Priam,
Hector’s mother wept. Then she undid her robe,
and with her hands pushed out her breasts, shedding tears.
She cried out, calling him—her words had wings:
“Hector, my child, respect and pity me.
If I ever gave these breasts to soothe you,
remember that, dear child. Protect yourself
against your enemy inside these walls.
Now, that could be a common custom, but it could also just be a poetic, dramatic gesture of a mother mourning her son before saying, "If I ever gave these breasts to soothe you,/Remember that, dear child".
As your Wikipedia notes, there is also a mention of bearing breasts and mourning in Herodotus, but that's for Egyptian women. The full quote is:
II:85. [The Egyptian] fashions of mourning and of burial are these: Whenever any household has lost a man who is of any regard amongst them, the whole number of women of that house forthwith plaster over their heads or even their faces with mud. Then leaving the corpse within the house they go themselves to and fro about the city and beat themselves, with their garments bound up by a girdle and their breasts exposed, and with them go all the women who are related to the dead man, and on the other side the men beat themselves, they too having their garments bound up by a girdle; and when they have done this, they then convey the body to the embalming.
I don't think this was a common mourning symbol in ancient Greece so I don't think that the early American and French revolutionary figures who imagined Liberty/Justice/Columbia/Marianne had this in mind. Why exactly they chose to depict these female embodiments with breasts exposed, I cannot say though.
I don't think there is any specific symbolism for one breast vs two, nor any specific association with Liberty / Justice.
For example, probably the most well known painting of Liberty is Liberty Leading the People by Delacroix, where she has both breasts exposed. Her being semi-nude is a form of heroic nudity. Basically it just tells us that she's more than human. That's also why she's depicted as being taller than the men. Heroic figures are shown with one exposed breast at times simply because they often wear a toga or toga-like dress, or a dress with straps.
The symbolism of anything you see will be different depending on the culture that created it, and many times misinterpreted in the future due to changes in cultural values. Many times artists will copy the iconography from a previous period in art and not know exactly what everything symbolizes, or change the meanings. Female nudity in one period's culture might be a symbol for power and free will, while in another it might symbolize sexual objectification, while in another it might be peace and pacificity. Another artist might cover up a goddess and paint her with no nudity at all because he belongs to a society that doesn't accept nudity in art.