You probably are going to need to provide a bit more info about which kit you are using and how you are using it.
I used to use a D300 with a Sigma 300mm f2.8 with a 2x converter and found that with the converter the Auto Focus was not hitting the spot. Manually focused it was good, better still if stopped down a little.
Give us a little more info about exactly which kit you are shooting with and i'm sure there will be some helpful advice.
In the mean time, why not just do a focus test and see if the lens behaves under zero wind / shake, on a tripod and preferrably using a cable / remote release. This eliminates a lot of possible factors just to see if it's a kit problem or a technique problem. I normally shoot at text of some kind where it's easy to see if it's sharp or perhaps grab a focus test sheet from online, I'm sure you can download one.
*edit to add* - Also be aware that warblers and small birds flitting around in bushes are a nightmare for autofocus as it's often difficult to keep the autofocus point(s) on the subject. From memory I think (i'm at work so can't check settings)I use 9 points AF rather than the 51 available so I have a little more control over which part of the scene the camera will attempt to focus on.