The simple way to do this (Photoshop CS5/5.1) is:
Step 1: In the Layers panel, Ctl(Cmd)-click on the thumbnail of a raster or shape layer that is the full size of your button. That gives you a selection that is the exact size (and position) you want.
Step 2: Edit > Copy or use Ctl-C.
Step 3: File > New or Ctl-N, and click OK. You now have a new document that is the exact size of your layer.
Step 4: Switch back to the original document and target the layer group in the Layers panel.
Step 5: Using the move tool, drag from the document (not the Layers panel) to the tab for your new, empty document. The focus will switch automatically to the new document.
Step 6: Hold down the Shift key, move the cursor onto the new canvas, and let go the mouse button.
All of your layers will import intact. You can then delete the background layer.
NOTE 1: In the case where you have effects applied, such as drop shadows, outer glows, etc., first convert the effects to layers. (In the Layers panel, right click on the word "Effects" under the layer name, and choose "Create Layers" from the menu.) Do this first, so your new document will have the dimensions to include the whole of the glow or drop shadow.
NOTE 2: Use "COPY" or "COPY MERGED" in Step 5 if you want a flattened image in the new document. To bring in the selected layers intact, deselect, then drag from the image window (NOT the layers panel) up to the new document's tab. When the focus switches, drop inside the new canvas while holding down Shift.
If you're using CS4 or earlier, follow steps 1-3, then copy and paste the layers one at a time.