Are you tired of hearing about battleground states, those portions of the country which so much cannot make up their minds that they are visited time and again by our political candidates? You should be, since we’ve been hearing about these kinds of states for quite a long time. How long, you ask? Well, put it this way, the earliest citation for battleground state comes from a time when the Whigs and the Locofocos were still experiencing their heyday in American politics.
Noble New Jersey!—The gallant Whig “Battleground state” still marches on in the steadfast maintenance of her exalted and unstained character as a hand of law and order….It is evident that the infamous outrage perpetrated on the electors of that state by the outcast Locofoco majority in the Twenty sixth Congress will never be forgiven or forgotten by the indignant Jerseymen.
—Centinel of Freedom, 15 Nov. 1842
To be honest, it isn’t entirely certain that the newspaper above is using battleground state in the same exact sense that we us today, but within another decade or two the phrase had definitely taken on the meaning of "a politically divided state which is likely to determine a close election."