$199 and they’ll replace it.

the Genius Bar will tell you what needs to be done before anything is done. I would just take it in and find out.

I was wondering if anyone knows or can guess anything in advance (it’s a long way to a genius bar for me).

They will replace it one time before charging you the $199, as long as it is currently within a year of the purchase date (or within a year and a half if you bought the AppleCare plan), at the discretion of the Apple employee you deal with. I suggest being cute and/or crying; it worked for me.

Have you tried rebooting the phone? My 3GS has a similar issue where the sensitivity of the home button degrades over time, and a restart gets it working again.

I am not absolutely certain about this, but since it is out of warranty and you are responsible for the repairs, I really doubt that they would simply swap it out with a factory refurbished model, because true Apple “factory refurbished” models still have a lot of value, and I strongly suspect Apple is not going to hand them out that casually.

When an iPhone is covered under Apple Care, Apple, I believe, has the option of either repairing your phone or replacing it with a factory an equivalent refurbished model and they are also sold by the services providers like AT&T. That’s where Apple is going to put their inventory of refurbished phones. If the button on your phone is a $100 repair, they’re not going to swap out yours, on the spot or at all, I don’t think, with a $500 refurbished phone. (just tossing out those numbers as an example. I have no idea what that kind of repair would cost and how much a factory refurbished iPhone is worth depends on how much memory it has).

That’s just what seems to make sense to me, but I could be wrong.

FYI, I ended up finding a perfectly good repair service (not affiliated with Apple) that repaired the button for $40—if you have this problem out of warranty, check for those options.