No. My phone holds about as much personal data as my house does. Opening that up for random at-will searches completely destroys any form of privacy
American law enforcement has long advocated for universal "kill switches" in cellphones to cut down on mobile device thefts. Now the Department of Justice argues that the same remote locking and data-wiping technology represents a threat to police investigations–one that means they should be free to search phones without a warrant. More: wired.com.
Its been stated by others, but it needs to be emphazised, that if arrested on other evidence, the phone can be secured and a warrant obtained. On the other hand, stopping someone who looks "suspicious" then checking their phones would be out of line.
I, personally, feel that if the police were allowed to search cell phones without a warrant that it would allow them to skip the trial by jury. Because, if we think about it, if we have incriminating evidence before a trial starts, the police can just say "Well, your phone says 'this'." Which, in my humble opinion would not allow the accused (key word, accused) a fair trial. Also, it could escalate to "Well, this was on your phone which we searched on the spot, so you're going to jail." If the officer has a warrant, then they have my permission to search my phone, lest they think I'm hiding something.