My daughter's dog has a stubborn tick on her back and it's so deep, I can't get a firm grip to get it out.  Any expert tips to remove it without detaching the head?  

I put neem oil on it directly, but you prob don't have that around you unless you have an organic food store nearby.  It will kill the tic and sooth the wound and then you should be able to remove it.

According to the CDC they say:

Tick Removal

If you find a tick attached to your skin, there's no need to panic. There are several tick removal devices on the market, but a plain set of fine-tipped tweezers will remove a tick quite effectively.

How to remove a tick

1. Use fine-tipped tweezers to grasp the tick as close to the skin's surface as possible.
2. Pull upward with steady, even pressure. Don't twist or jerk the tick; this can cause the mouth-parts to break off and remain in the skin. If this happens, remove the mouth-parts with tweezers. If you are unable to remove the mouth easily with clean tweezers, leave it alone and let the skin heal.
3. After removing the tick, thoroughly clean the bite area and

Avoid folklore remedies such as "painting" the tick with nail polish or petroleum jelly, or using heat to make the tick detach from the skin. Your goal is to remove the tick as quickly as possible--not waiting for it to detach.

According to a Vet site:

Removing a tick from your cat or dog is easy if you just follow these simple steps.

To remove an attached tick, use a pair of fine-tipped tweezers or special tick removal instruments. These special devices allow one to remove the tick without squeezing the tick body. This is important as you do not want to crush the tick and force harmful bacteria to leave the tick and enter your pet's bloodstream.

1. Grab the tick by the head or mouth parts right where they enter the skin. Do not grasp the tick by the body.
   
   
2. Without jerking, pull firmly and steadily directly outward. Do not twist the tick as you are pulling.
   
   
3. Using methods such as applying petroleum jelly, a hot match, or alcohol will NOT cause the tick to 'back out.' In fact, these irritants may cause the tick to deposit more disease-carrying saliva in the wound.
   
   
4. After removing the tick, place it in a jar of alcohol to kill it. Ticks are NOT killed by flushing them down the toilet.
   
   
5. Clean the bite wound with a disinfectant. If you want to, apply a small amount of a triple antibiotic ointment.
   
   
6. Wash your hands thoroughly.

Please do not use your fingers to remove or dispose of the tick. We do not want you in contact with a potentially disease-carrying tick. Do NOT squash the tick with your fingers. The contents of the tick can transmit disease.

Once an embedded tick is manually removed, it is not uncommon for a welt and skin reaction to occur. A little hydrocortisone spray will help alleviate the irritation

Hunger, thank you for your response, but I got it.  Searched here and found a simple and effective way to remove it and it worked!  I'm amazed how easy it was!  Here's a link...
http://www.instructables.com/id/How-to-remove-a-tick/

Wow!!! Thanks! I never would have believed that would work until you posted that and tried it.  I am going to save that (hoping never to need it.)  I wonder how they even thought of that!?

I don't know, but it worked like a charm and he came out intact!  Took about 10 seconds! 

Cool, thanks for posting that video... that was cool.

Place a drop or two of strong cinnamon bark oil directly on the tick, the tick will back out and then you knock it off and can squash it.

Well thanks, I'll have to try that technique. We found a nasty little beast deeply attached to my daughter's neck a week or so ago that was hard to remove. I wish I'd know this then....