I think you're trying to move the wrong element left/right. I think you need to leave your sheep in the middle of the screen then move the background.
Something like:
var walkLeft = function() {
$('#background').animate({left:"-=10px",top:"-=2px"}, 100);
$('#background').animate({left:"-=10px",top:"+=2px"}, 100);
};
var walkRight = function() {
$('#background').animate({left:"+=10px",top:"-=2px"}, 100);
$('#background').animate({left:"+=10px",top:"+=2px"}, 100);
};
http://jsfiddle.net/CkkVr/22/ (you'll need to "jump right" to see the sheep), but you get the general idea!