If your rear tire seems 'soft' when rolling @ 120psi, I would suppose any tire at that pressure would seem just as 'soft'. Just get your LBS to tension your current wheels properly for now. Some semi-loose spokes are normal in some wheel builds.

As far as feeling safe on the wheel, the worst that could happen would be a popped spoke, and that would just make your wheel wobble a little bit more - it wouldn't be dangerous - just put some wire or tape in your saddle bag in case.

Out of curiousity, how many holes/spokes are in the rear hub?