So, you say "no", and they they tow your car to search at the police station. You haven't won anything.
Either that or they’ll bring in a dog. They can make the dog “hit” anytime they want. Now you’re under arrest and you’re car is being towed. Cops are out of control in this country. And if the SHTF, don’t count on them to be on your side.
Sure, they might go get a warrant, or call in the dogs to sniff around and give them a signal, or just search it anyway based on some invented “probable cause”. Still, if you give consent, they don’t have to go through that rigamarole, so you are giving up whatever chance you might have had to avoid a search. Also, you’ll have little recourse if they do find something and you have to try to contest it in court. If you refuse, a good lawyer can at least make a decent case that the search was improper and try to get that evidence thrown out.