The wonder of Laura Robson's American odyssey is not so much whether or not she can beat the defending champion, Sam Stosur, and advance to the quarter-finals of the US Open (she can), it is the clamour building for her to go even further. This tempting of fate is not a particularly British disease, but it has been raised to an art level through years of great expectations, nowhere more starkly than in tennis, a sport so beguilingly beautiful that its serial disappointments for home-grown players seem all the more poignant.

Robson was asked by an American journalist before she played Kim Clijsters, a three-time champion here, if she felt the burden of a nation's demands for success given that, well, the British are rubbish at the game they invented. She smiled, shrugged, toyed with the microphone and pretty much blanked him out. For Robson, history is not an issue – even her own. She came to prominence in the most charming way, a young and virtually unknown teenager, the daughter of Australian parents who had landed in the UK when she was six, a girl with a booming forehand and nothing to lose as she beat Noppawan Lertcheewakarn 6-3, 3-6, 6-1 to win the girls' title at Wimbledon four years ago.

It seems longer ago than that, as if the Laura who beamed for the cameras that day was a different person, a 14-year-old kid thrown into a media maelstrom of someone else's making – the someone else being all those who had gone before and failed. Now she had changed a little bit of that history.

Yet, then as now, she was brilliantly unimpressed. She was happy, naturally, to have won and glad to have pleased this new audience, a nation waiting for a hero to rescue them from their pain. But, essentially, she was still just Laura. When she won, she did something odd: nothing. She just won. And smiled.

Asked later about her reaction, she said: "I hadn't really thought about what I was going to do if I won, because it was so unexpected. But my brother was telling me, drop to your knees, start dancing, do something. But it was just on the spot and then I couldn't think of anything to do."

So, the American reporter got just a look, a half-smile and a shrug that said, if you want to worry about that, go ahead. I'm just here to play tennis.

When she beat Clijsters, Robson smiled again, as achingly long as it is possible. When she beat Li Na, the ninth seed, she did the same, mouth open as much in joy as in minor disbelief. The disbelief is minor because, she does not have any doubts about her talent.

Asked how she might play Stosur, whom she has hit with but never played in competition, she did not have to think about the answer for long. "I will just play my shots."

That is the beauty of Robson's tennis: it is uncomplicated, uncluttered, natural. It is far from perfect. There are moments when her muscular arm rolls through the stroke and the racket strikes the ball with the force and precision of a champion, sending the ball unerringly in the right direction. When that movement is fraction off, when her feet are rooted to the ground in the wrong place and her balance is awkwardly miscued, the ball can go just about anywhere.

Clijsters and Li testified that there was little they could do when Robson unfurled her power. Stosur, no delicate flower on the court herself, has no doubts either what to expect: "She will come out swinging. She has nothing to lose."

That is it in a sentence: Robson has nothing to lose, but those who heap their hopes on her young shoulders do. They are investing in her not just their good wishes but their demand that she deliver for them.

If she can, she will. Stosur might be the perfect opponent for Robson, a fragile talent, despite her muscularity, a player who is the polar opposite of the teenager in that she does not entirely put her faith in her gifts. She has had moments when she has looked irresistible – as when she mastered Serena Williams in the final here last year – and others when the ballkids could probably have beaten her, as when Francesca Schiavone emerged to beat her easily in the French Open final.

Not many outside the game's hardcore had heard of Schiavone before that brilliant summer's day. A lot of people, though, have heard of Robson. If she beats Stosur, that audience will grow considerably; if she dares to toy with our expectations and get past the quarter-finals ... well, it doesn't bear thinking about. Unless you're Laura Robson.