use a dremel and drill a slot in the bolt head. Then use a standard screwdriver to remove it. Maybe squirt some lubricant and let it loosen up a bit first if it's really bad.

Aside from what Uncle Phil suggested, is the head stripped or the threads, or the pop rivet loose? Can you turn the bolt, but it won't come out? If so, then the rivet inside is loose. You'll need to both turn the bolt and pull it at the same time (to keep the rivet from turning).

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"Go yell at an M&M"

This looks like what si happening. I have 2001 QR TiPhoon an it looks like the bosses (?) that are inserted into the TI are turning.

I assume that this is not good.

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This is your life, and it's ending one minute at a time. - Fight Club
Industry Brat.

I've had this happen, and any good shop should be able to get the bolt out. I'd guess it's a matter of holding the rivet (that's the thing in the seat tube) in place while turning the bolt. If there's any part of the rivet that you can get a grip on, you can hold it with a pair of vise grips or equivalent. If not, you might be able to squeeze something (like wrapping thin wire around the bolt and pulling it tight so that it goes under the cage) between the cage and the rivet. Keep wrapping the wire to fill the space as you back the bolt off.

A trick that you should use when you get the bolt out is to put a nut onto the bolt, then thread the bolt back into the rivet until the nut bottoms out on the rivet. Hold the nut in place with a wrench, then back out the bolt. This will pull the rivet tight against the seat tube. Remove (or not!) the bolt, remove the nut, and re-insert the bolt. This avoids having to put in a new rivet (I think you need a special tool for that).

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"Go yell at an M&M"

That is a simple repair for a quality shop. They should be able to pop in new threads much like a rivit.

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What if the Hokey Pokey is what it is all about?

Ahhh..that's different than a stripped bolt. By all means do as the others have suggested.

you can always buy a new headset from www.cyclinginnovations.com or just a new headset bolt!