Three days is the practical minimum if you want to see both the Roman north and the Sahara, because Tunis to the desert is about 426 km in a straight line and rather more by road. One day is enough for Carthage, Sidi Bou Saïd and Tunis. A week reaches most of the country. Fifteen days is what it takes to stand in 9 of Tunisia's UNESCO World Heritage sites — every one currently open to visitors.
For one city, yes. Carthage, Sidi Bou Saïd and the Tunis medina fit comfortably into a single day and are within 20 km of each other. One day is not enough to reach the Sahara, El Jem or the mountain oases.
Two days minimum from Tunis or Hammamet. The drive is roughly six hours each way, so a single day would be twelve hours in a car for perhaps an hour in the dunes.
A week covers the north and the south: Carthage and the Tunis medina, the Roman cities of Dougga and El Jem, Kairouan, the Chott el Jerid salt crossing and the dunes at Douz, with time to stop properly at each.
Distances are straight-line, measured between the coordinates on our map of the sites; road distances are longer. Prices are per vehicle and come from the same database the 28 tours and 1,392 transfer fares are quoted from.