For anything. Don’t give permission to search your car. Don’t give permission to search your house. Don’t give permission to look in your trunk. Don’t give permission to look in your pockets.
Tell the police officers that you won’t give permission for anything without speaking with your lawyer. If you give “your consent” to something your lawyer typically can’t complain about it later. If you give your consent to search your house, for example, your lawyer can’t complain that the police had no right to be there, or that the warrant was defective, etc…
The law regarding searches and seizures is amazingly complicated. It is also changing constantly. I regularly have to look up the law to see how it has changed or how it could, would or should be applied in a particular situation.
If you give your consent to anything, it is usually impossible for your lawyer to challenge the validity of it later. Police officers have to make legal judgments in a snap. It is hard job and mistakes are inevitable. Just because they say that they could get a warrant (for example) doesn’t mean that they can (or will).
Officers love when suspects give consent. It usually means that they won’t have to worry about the evidence they find being thrown out of court for legal reasons.