Try printing to other printers and see what results you get. it has been my experience that different printers and different printer drivers can have a real impact on label printing.
Using that testing as a guide you can get into Layout mode and select and move the labels object very slightly to the right and if possible very slightly reduce the size of the label object itself.
If that does not work then look at the number and size of the merge fields used on the layout; there may be some space savings from concatening the individual data fields into a single calculated label field.
One last thing - look carefully at your data; you could have "dirty" data - data loaded with tab characters, carrage returns, spaces, etc. that can really mess with you.
If moving layout objects around doesn't work, you can also go to Layouts > Layout Setup, and then to the Printing tab. If everything is off by the same amount in the same direction, adjusting the margins is a great way to correct it. If everything is printing too far to the left, then I would make the left margin larger.
I've also found that it's best to make one change at a time, and then go back to Browse mode to see what the effect was each time. If you make too many changes at once, it could make the problem worse, and then you'll have a harder time trying to figure out which change to undo. It's also a great way to get better at adjusting print layouts that can be a little finicky (like with name badges and labels).
First thing to check is that the label field or text object is not itself positioned of the label area. Assuming that is correct you could try adjusting the padding in the label field (or text object)—see Advanced Graphic in the Appearance Inspector. A bit of left padding will nudge the text to the right.