Where did you get these lyrics, Chico? I take it that they're from the election of 1904, after Roosevelt had become President after the assassination of McKinley. The one election songbook I have, Songs America Voted By, has lots of Roosevelt songs, but not that one. However, the book does have a Roosevelt song that mentions David Bennett Hill - I'll bet that's the Hill your song refers to.

Bartleby.com has this entry on Hill:

Hill, David Bennett

1843–1910, American politician, b. Montour Falls, N.Y. He entered law and politics, becoming the upstate boss of the Democratic party in New York. He served as state legislator and, as lieutenant governor, succeeded to the governorship in 1885 upon Grover Cleveland's resignation. He was elected governor in 1885, and reelected (1888). As U.S. Senator (1892–97), he fought the free-silver wing in his own party.