You need to get your facts straight. Jefferson's party was the Democrat-Republican party. The modern Democrat party was created when the Democrat-Republican party split over the issue of slavery in 1860. Don't believe me -- WIKI it.
And this nonsense about the Republican party favoring big government is only true it you believe the American government didn't have the right to stamp out slavery -- because the southern states had a "divine right" under the 10th amendment to enslave half their citizens. In other words, just more Dumbocrat gibberish.