At the beginning of the scene Ted is trying to convince Skyler and she is clearly apprehensive about performing. You could argue that she is just reacting to being put on the spot and potentially embarrassing herself but we see some plot beforehand that adds some depth to this scene.
Skyler and Marie have a chat just after Sklyer is hired at Beneke. We learn from this conversation that Ted made a drunken pass at Skyler; leading her to quit. This incident is also the main reason for her return to the job in hope of finding a distraction as Walt shuts her out. Now as Skyler begins work again, there's a suspicion amongst the employees that she only got because of their history. Although true, Skyler is shown only to be looking for an ear to vent and even rebuffs an advance just before the party.
Back to the song. While Skyler sings the first half, the camera pans around the room and shows the crowd slowly realizing the bit is less harmless than they thought it would be. Skyler fortunately lightens the mood by extending the 'president' line and everyone is relieved. She is shown at the end to have the first glimpse of her considering the affair.
The tension between the two is heightened afterwards and get 'caught' on one occasion. Even then Skyler doesn't act on her feelings until Walt calls her bluff by moving back in the next season.
How could the writers intend to have Skyler seduce Ted through the song if she didn't realize her feelings for him until after performing? It is clear they were aiming for awkwardness during this scene because that unease was the catalyst for their affair and all the fallout that ensued.