Dec. 13, 1862 is when the Battle of Fredericksburg was fought. The poem would have been written later.
The article by Warren, "Oh, What a Pity," in the journal, Civil War History, as cited above, may help. And that poem in the 1863 Pittsfield, Mass. paper- is it the same poem?. It is difficult and expensive to find information without university research facilities!

I believe Jim Dixon is correct- These seem to be lines from O'Reilly's poem:

AT FREDERIKSBURG, DECEMBER 13, 1862

God send us peace, and keep red strife away, But
should it come, God send us men ans steel! The land
is dead that dare not face the day When foreign
danger threats the common weal.

Defenders strong are they that homes defend;
From ready arms the spoiler keeps afar.
Well blest the country that has sons to lend
From trades of peace to learn the trade of war.

http://www.traditionalmusic.co.uk/gt-irish-songs-lyrics/golden-treasury-of-irish-songs2%20-%200331,htm

Probably written after O'Reilly became a friend of Walt Whitman's and absorbed his Civil War poems.

Digression-
Remarks by John F. Kennedy, 1957, speaking of Soviet actions in Hungary:
"I know of few men in our land, and none in this room, who would ignore these tyrannies as far-off troubles of no concern to us here at home. For we realize, as John Boyle O'Reilly once wrote, that:

The world is large, when its weary leagues
Two loving hearts divide;
But the world is small, when your enemy
Is loose on the other side."
............
Kennedy goes on to speak of the "Wild Geese,"- the officers and soldiers forced to flee their native Ireland after the Battle of the Boyne; he speaks of the Irish who broke the ranks of the English at Fontenoy, who fought with the Spanish and turned the tide of battle against the Germans at Melazzo, "and fighting for the American Union Army, they bore the brunt of the slaughter at Fredericksburg"
(It should be mentioned that the Army of the Confederacy also had many Irish immigrant soldiers).