Third parties want to sell as many full-priced copies of their games as possible for as few platforms as possible. Previously, third parties had an interest in promoting a new gen, because the extra features and power allowed them to do more with their games which would stimulate sales. Porting new games to the previous gen was impossible or would present an incomplete experience.
Next gen is different. The PS4 and 720 will not be much in power above the current gen, insofar as they both can display realistic worlds in high-definition. An Assassins Creed that was developed for 720, if backported to 360, would lose some effects, shaders, lines of resolution, and texture quality but it would be fundamentally the same game and the same experience in the way that a PS3 game ported to PS2 would not.
The 360 and PS3 represent a 140m installed base of the buyers third parties want. When next-gen launches, even at full capacity there will only be 5-10m sold in the first year. When a publisher is making a market decision about which platforms to go for, they will have to launch PS3 and 360 versions of their new titles at the first and possibly second Christmases of next-gen. Call of Duty certainly will. With such little difference between the gens, people might be willing to pay a little extra but, in this economy, not a whole $400 console extra to get the improved graphics. On installed base alone we will see people overwhelmingly choose the 360 and PS3 versions.
Third parties will see this, see their games in development and the ease of backporting by changing a few quality settings, and continue to release PS3 and 360 versions of the important titles. They have no obligation to MS and Sony to support their next gen launches. Then PS4 and 720 will lack killer apps and effectively, as we see with Wii U, be competing with current gen consoles for the same games, which they will surely lose. The smaller third parties may not even want to move to the increased budgets and smaller installed bases of next gen at all.
It will be up to first party titles to persuade customers to purchase PS4 and 720.