I think publishers will find a way to follow the new rules if Apple remains firm on the new guidelines. iOS is to big a market to miss out on.
This is simply not possible. Let's say you have a widget that costs you $7. You sell this widget for $10, because that is the price you are contractually obligated to sell it for. The remaining $3 covers your overhead, the cost of maintaining and delivering the stock of that widget, plus a small amount of profit.
Now, a new restriction comes along that you must give $3 on every sale of said widget to a third party. So of the $10, you're giving $7 to the manufacturer, and $3 to an unrelated entity. Leaving you with $0.00 to cover your overhead, stocking, and delivery expenses, let alone offering a profit.
You are now contractually obligated to lose money on every sale you make, and there is literally nothing you can do except stop selling. Which is exactly where Amazon and Barnes & Noble are under the new rules. They have exactly two choices--lose money on every book sale to an iOS user from now until the end of time, or stop selling on iOS. There is no middle ground.
Rhapsody is even worse off, since their widget costs them $8, they sell it for $10, and still have to pay the $3. So their losses on the sale alone are now $1, even before overhead and expenses are considered. Yes, they do have the option of raising prices--$14 would get them back to roughly the same margins they had before, but they'd have to foist that increase on everyone, and that would cost them a LOT of customers. $12 is the breakeven point, where they make no profit before expenses are considered. The only smart move for them is also to exit the space.
Netflix is likely in about the same boat, but I don't have specific knowledge of what their widget costs as I do for the others, so I can't make an accurate example.