Take a look at your tuners. Chances are there is a piece of metal that fits around that actual tuner post. This is called a bushing. Many tuners do not get pressed directly into the tuner post or peghole. Many tuners are pressed into bushings. Bushings are basically spacers that help center and hold the tuner post in place. Without these bushings Grover, Schaller, and Gotoh tuners wouldn't fit properly in their pegholes. These tuners require that a bushing be pressed into the peghole before the tuners can be installed. Before your press the tuner bushing in, you must prepare the peghole.
After the peghole is laid out and drilled, it is ready to be counterbored. These tuner bushings only go about half way into the peghole. There is no need to drill the entire peghole with a larger drill. Instead, you can use a guitar tuner bushing reamer. This is just a reamer that counterbores the peghole. By counterboring the peghole, it helps stabilize the bushing while it is under string pressure. The lacquer under the bushings is also protected because the bushing is less likely to lean and crack the lacquer. The perfect counterbore is important because if the tuner is loose in its peghole, the tuner will rattle around and possibly fall out. If the hole is too tight, the bushing will crack the lacquer or wood when it is being pressed in.
To counterbore your peghole, simply load the reamer in your drill press. Place your peghead on a flat block of wood. Set the stop on the drill press to the accurate depth for your specific tuner. The reamer will pick up the predrilled peghole. Counterbore down to the stop and you are done. You have a perfect counterbore for your tuner bushing to fit snuggly inside.
A peghole reamer is a great tool to have. If you are installing tuners with bushings, you have no choice. You have to have one. If you try to enlarge the pegholes with a regular drill bit, you could chip or split the headstock. Then you will be thinking more about trying to repair the damage you did rather than installing your tuners. You are far better off having the right tool for the job. If you would like more information about how to replace guitar tuners, please see my how to replace guitar tuners article.