When actress Reese Witherspoon was arrested recently (seemingly for mouthing off to the police officer), many people started asking if it is a crime to mouth off, cuss, or yell at an on duty police officer. The answer is that technically it is not, but if you decide to speak your mind to the police, you shouldn't be surprised if you wind up getting arrested.
How can the police arrest you if you haven't committed a crime? Nobody likes to be cussed at, yelled at, or insulted, and cops may not only take it personally, they may also view it as a challenge to their authority and they can sometimes look for any way they can to make you pay. If someone is interfering with a police investigation, the officer can charge them with obstruction of justice (which in California is the same charge as resisting arrest), but the most common thing the police charge people who are being uncooperative with is Drunk in Public. You can be charged with Drunk in Public even if you haven't had a drop to drink. Unlike DUIs where the tests that establish your level of intoxication are very important, a Drunk in Public charge relies primarily on the officer's observations and assessment that you are unable to care for yourself - the same officer that you have just managed to piss off. Sometimes officers don't even care whether the charge sticks or not. They figure that even if you are ultimately able to get the charge against you dismissed, spending the night in jail, and having to go through the ordeal of fighting the charge is punishment enough for making their job difficult.
However, it is very important to remember that being cooperative does not mean you need to give up your right to remain silent and your right to an attorney. The trick is to invoke your rights while being as respectful and as cooperative as possible. I typically advise my clients to blame me. I tell my clients to tell the police that they would be more than happy to help them in any way they can, but that their attorney has advised them not to say anything without checking with him first, so they need to talk to their lawyer before they say anything. The police must respect your request to talk to a lawyer, but if you ask respectfully, it wont appear that you're being uncooperative.