I don't think he's superpowered at all he's just meant to be the ultimate human even the Red Skull appeared to be stronger than Rogers though being able to dent Cap's original shield.
But during those musical numbers, didn't they have Cap holding up a motorcycle with three girls sitting on it? I remember noticing that they had Cap trembling a little to show he was pushing it and it wasn't easy.
Also, the movie was pretty clear that Skull had received an early version of the super soldier serum. it was that faulty serum that caused Skull's cosmetic changes; but we're left to assume it gave him the strength and endurance too.