They'd probably harass you for carrying it... "And why would you feel the need to carry this around if you're not doing anything wrong? So you must be doing something wrong..."
And no matter how you try to answer, it would just escalate the situation further. In fact, virtually any answer you give to a cop other than "Yes sir" will usually escalate the situation. Forget about trying to assert your Constitutional rights - that'll get you a ticket to Rikers faster than anything else...
Besides, only anti-government lunatics like Tim McVeigh and the Unabomber, and those tree hugger wackos at the ACLU really care about their Constitutional rights. We have to uphold Fatherland Security after all, and if some of your rights have to be abridged that's too bad... that's not just the opinion of the Storm Trooper harassing you, but alas also of the general US population at large. "Oh, he must be doing something wrong if he won't consent to a body cavity search without probable cause to any jackass who requests it. Oh, why would he demand a lawyer or refuse to answer a question if he wasn't doing anything wrong? Well, if the officer decided to question him, he must have been doing something wrong." etc.