In Ireland the words are 'over here', while in America they're 'over there'.
The potato blight hit Irish crops for three consecutive years, which largely accounts for the severity of the Great Famine (there were social and political factors as well, of course) So it's usually dated as starting in 1845. The blight rendered potatoes inedible; if only they were merely small. But any small potatoes edible potatoes would have had to be eaten, rather than planted as usual to provide a crop the next year.
Whether or not this song actually arose from an Irish famine I leave for more knowledgeable Mudcatters to comment on.

PRATIES THEY GROW SMALL

Oh the Praties they grow small over here, over here
Oh the Praties they grow small over here
Oh the Praties they grow small,
And they're failing since the fall
So we eat them skin and all, over here.

Oh, I wish that we were geese in the morn, in the morn
Oh, I wish that we were geese in the morn,
Oh, I wish that we were geese
And when we had found release
We could eat away in peace in the corn.

But the God in whom we trust, over here, over here,
But the God in whom we trust, over here,
But the God in whom we trust,
He will give us crumb and crust
and he'll raise us from the dust, over here. ^^^