Scott Johnson's side have succumbed to limp defeats in their two matches so far, including a 20-0 loss to England at Murrayfield at the weekend, and have scored just three points.
The Scots will now limp over to Italy to face a team which has also succumbed in their first two fixtures in this year's competition - losing to Wales and France. It is likely Scotland's best chance of enjoying some sense of Six Nations success and Swinson is adamant that his team can deliver.
"The Italy game can be a turning point for us," the Glasgow Warriors forward said. "A lot of people are putting us on a par with the Italians but we want to be higher than that. We are not comfortable being in this position.
"We want to aim for the stars and really push on from this point so we are flying by the time the World Cup comes around next year. The game in Rome will be huge for us but there is no doubt about it, we will go there looking for the victory."
If that is to come true Scotland will need to make significant improvements to almost every facet of their game. The statistics from the loss to England were an indictment of Johnson's side - Scotland gave away 65% of the possession and ceded 76% of the territory in the second half - as the Australian put his faith in inexperienced players such as Matt Scott, Alex Dunbar and Duncan Weir.
Those players are expected to retain their starting places in Rome and Swinson is satisfied with his coach opting for consistent selection. "It's a process all teams go through," said the Scot, who has only earned five caps himself. "We have a lot of young guys in the side but we also have guys who have been performing at top level in the domestic game in the Pro12, the [Aviva] Premiership and the Top 14 [in France]."