While it might be better to job out major asphalt repairs, you can definitely manage smaller projects yourself, and this patch kit can help. The FloMix kits advertise no dig-out — just sweep away loose material, then mix, pour, and spread. You can apply FloMix even in sub-zero temperatures. According to the instructions, once the components are mixed you have 9-12 minutes to work with the patch compound, and the patch cures in one hour.
Note: You may want to get a mixer attachment for your drill if you don’t have one — the video on the site makes it look easy with the power mixer, and I’m guessing that using a paint stirrer would be an exercise in futility.
A three-gallon kit runs $66 and a five-gallon runs $98, or you can get the pallet if you need that much. Keep in mind: the FloMix kits aren’t the only game in town. You can find less expensive kits and kits for more specific applications. But it looks like it would be hard to go wrong with FloMix, even if it might be overkill.