Should not be any barrier to store acceptance. It is really up to you to decide what you want to say it runs on. If you choose to say it is OK for a Touch you can probably bet it isn't the worst performing app, but you should think carefully about what kind of experience you are delivering and whether that could hurt your reputation or repeat business long-term. Plenty of apps do not target the Touch of course because it lacks some of the iPhone hardware.
Consider detecting what hardware you are running on and switch to a reduced mode (i.e. a word game could use a smaller word list, a search could be enter terms and submit rather than dynamic) if you detect that you are on hardware that will not cope well with what you are trying to do.
In another answer Will Harris gave this code for detecting what hardware you are on:
#import <sys/utsname.h>
NSString*
machineName()
{
struct utsname systemInfo;
uname(&systemInfo);
return [NSString stringWithCString:systemInfo.machine
encoding:NSUTF8StringEncoding];
}