Google recently optimized for the hundredth time, the Google Search experience on the iPhone and also Android. But it seems like ever since the upgrade, many iPhone and iPod Touch users are having issues searching at Google on mobile Safari.
A Google Mobile Help discussion thread has bug reports from several iPhone/iPod Touch users complaining they can no longer conduct searches in Safari on Google.
I tried this on my iPhone and it worked fine for me. So hopefully it is now fixed.
Forum discussion at Google Mobile Help.