We've known for a while that Qualcomm can't keep up with the demand of the S4 processor, in a time when they would need as much supply as possible, considering they were in short supply even before the Galaxy S3 was going to launch in US, and now that it's about to get launched in US, and that Galaxy S3 will use only the S4 chip in US, it will get even harder for Qualcomm to keep up.
But Qualcomm is working hard to fix this solution, and one way it's going to do this, is by expanding their partnership with other foundries, like UMC for 20-30% of the output of TSMC for the S4 processor, and it's also looking into signing a deal with Samsung, one of their competitors in the market, but also one of their partners, considering Samsung has used their chips in the phones in the past, and of course they are going to use the very same chip that Qualcomm wants them to manufacture, in their US version of Galaxy S3.
Samsung is no stranger to manufacturing chips for others, one of the most popular cases being how they are manufacturing chips for their biggest competitor in the market - Apple. It's not certain whether Apple wants to move away from Samsung's components yet, but we've heard some rumors since last year that they want to switch to other manufacturers. This may have changed since Tim Cook became CEO, but Samsung is still preparing to get other clients on the side, in case Apple does stop making chips in their foundries.
Since they are just now signing these deals, it might take until the end of the year until Qualcomm gets its S4 production increased, and until it catches up with the demand. By then we might see Samsung's own Cortex A15-based processor try to compete with the S4, and might still just enough customers from Qualcomm, that they won't have to worry about too high demand anymore.