In the US a Republic was the least bad alternative to being ruled by a foreign monarchy, even if that monarchy was the government of your ancestors.  There were oligarchic republics like Venice as examples, but they did not inspire or truly fit the American situation.  So they took ancient Rome as a prototype and tried to strengthen the protections for individual liberty through  structural refinement--divided government.  Extension of the franchise mostly arose out of local governments established as the nation spread westward.

Jefferson envisioned a republic of small land holders, and Jackson was the proponent of the "backwoods" everyman who he mobilized in the service of westward expansion, relocation of Native Americans in the service of real estate developers and the expansion of slave holding practices.  Lincoln was a great proponent of "government of the people, by the people and for the people," but freeing the slaves was a strategic act of war rather than of principle.  The Radical Republicans tried to extend the franchise to emancipated blacks during reconstruction but worship of money prevailed under Grant and Jim Crow emerged in the South.  Women had to wait until the 20th century except in the west. Native Americans, whether their first European language was English, French or Spanish, had to wait until the second half of the 20th century.  Democracy for whom?

As the Dutch said while fighting the Spanish: "It is not necessary to have hope in order to persevere."