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Samwise Gamgee never became corrupted by Sauron's One Ring, despite much stronger Lord Of The Rings characters falling to its influence. This says a great deal about Sam's character since he clearly possessed a certain quality that kept the Ring from gaining control over him. While this is true of most Hobbits, to some extent, the gentle gardener was uniquely equipped for his job to support Frodo Baggins' in his perilous journey. He might have been even more resistant to the Ring than Frodo himself, hinting that he might have been a great Ring-bearer.
While on his journey in The Lord Of The Rings, Frodo quickly learned how dangerous The One Ring could be. Though Boromir never carried the thing itself, he was still corrupted by it and uncharacteristically attacked Frodo to get his hands on Sauron's dark weapon. From then on, Frodo trusted no one and decided that the only thing he could do was depart from the Fellowship to ensure that no one else fell prey to its influence by proximity. Of course, Sam wouldn't take no for an answer, and he came along anyway. Thankfully, he was never even tempted to take the Ring for himself.
Sam's lack of traditional ambition was unique to his character, but he was predisposed to such traits as a Hobbit. Though halflings are believed to have evolved from Men, they lack the desire for power that the big folk commonly possess. They are described as simple folk who delight in the earth and all things that grow. Food, drink, pipeweed, and peace are the things they most aspire to, and they know that a little hard work and cooperation are all they need to achieve it. It's for precisely this reason that Gandalf became so fascinated with Hobbits.
The Appendices of The Lord of the Rings: The Return of the King reveal that Gandalf first discovered the Hobbits during the Long Winter, centuries before the events of The Fellowship of the Ring. It was then that he realized just how much the powers of Middle-earth overlooked these beings. Later, the wizard knew it was no coincidence that a Stoor like Smeagol had kept the Ring for so long or that a Hobbit like Bilbo had found it. Destiny had chosen Hobbits as Ring-bearers, and though Sam didn't carry the Ring for long, he was destined to assist Frodo on his journey.
Given Sam's strength and purity of heart, there's no question that he would have been able to carry The One Ring for the long journey to Mordor without being taken over entirely by it. However, if he had been the Ring-bearer, something would have been missing—he wouldn't have had a Sam to support him. Frodo did a remarkable job carrying the Ring, but no being in Middle-earth could have made that journey alone. In the end, he needed a pure and hopeful friend by his side, or the One Ring wouldn't have been destroyed.
While Frodo would have done his best to support Sam had their roles been reversed in The Lord of the Rings, there's no guarantee that things would have gone the same way. Frodo and Sam were the perfect team, and the Ring-bearer needed Sam's love and purity to pull him back after such a horrible experience. Sure, Frodo still had to leave for the Undying Lands to relieve his pain, but he wouldn't have even made it that far if it wasn't for Sam. Were the roles reversed, who knows how That Lord of the Rings would have ended.