Lets say a person has been "Terry Stop"ed. The person does not carry any id with them. As the Police continue to question the individual, he advises them that he will be remaining silent and not answering questions without an attorney present. The police don't have any probable cause for an arrest but are annoyed by this persons refusal to cooperate. They decide to charge the person with "obstruction of justice" and arrest him. Is this a legitimate arrest?
On the facts given, no. The relevant statute is at http://www.leg.state.fl.us/statutes/index.cfm?App_mode=Display_Statute&Search_String=&URL=0800-0899/0843/Sections/0843.02.html:
843.02 Resisting officer without violence to his or her person.—Whoever shall resist, obstruct, or oppose any officer as defined in s. 943.10(1), (2), (3), (6), (7), (8), or (9); member of the Florida Commission on Offender Review or any administrative aide or supervisor employed by the commission; county probation officer; parole and probation supervisor; personnel or representative of the Department of Law Enforcement; or other person legally authorized to execute process in the execution of legal process or in the lawful execution of any legal duty, without offering or doing violence to the person of the officer, shall be guilty of a misdemeanor of the first degree, punishable as provided in s. 775.082 or s. 775.083.
However, the refusal to answer questions is protected by the fifth amendment to the US constitution, so the refusal cannot be construed as resistance, obstruction, or opposition to the lawful execution of a duty.