If your 360 has stockish pistons, then the cam won't be too much for the engine in terms of detonation problems or anything like that. But it might be too much in terms of lowering torque at the low RPM range. with a stockish type of torque converter and too low of a CR with too big of a cam, then what will tend to happen is that the engine will bog as you try to take off, will just kinda lazily rev up to a certain point, and then take off. For street use, that will be an unhappy combination as that is where you want to do a lot of driving: lower RPM ranges.
The typical solutions are to
1. Raise compression ratio (piston change) to recover the lost low RPM torque and widen the torque curve
2. Raise the stall speed of the TC (TC changeout) so that the engine revs past the bog range and gets up into the good RPM range when you take off. The higher stall speed can have some adverse effects on mileage and trans heating.
3. Use a different cam named a torque cam that has lower duration numbers but keep higher lifts. The Lunati Voodoo cam series like you have is about as good as that gets in a hydraulic lifter cam. A lower duration version would get past the bog.
For street, I'd go for 1 or 3 above, but opinions vary as to what constitutes 'street use'. And this is all predicated on you have a lower compression engine to start with.
Have you run any compression tests on the engine? And do you know if the cam is stock? If so, a compression test will give a general idea of what CR you have.