If only it was that simple.
The facts are, normal unclipped music material has a RMS:Peak ratio of about 10dB - slightly lower on stuff heavy in the bass, and more on vocals. Your amp needs to pass the peaks of the music undistorted, whereas the total power used from the powersupply is the average. The car amps have a DC-DC voltage step up in them which averages out the powerdraw nicely.
So, your 120w peak speakers, on normal music will be outputting about 12 watts RMS, quite loud as anyone that owns some mcintosh audio gear with wattmeters will tell you

Most sony and other mid to lo-fi stuff measure it with a single tone at 1kHz at medium distortion levels (0.5-1%), and the sine waves RMS is only 3dB less then the peak power they will get from the voltage in the amp, so they get another 7dB on that rating over what you will actually be pushing thru it with normal music material.
If your not entering bass sound offs, you wont be playing anything remotely like that, so your 300 watts becomes something closer to 30.
PMPO is BS'd furthur by measuring the instantanious power as the amp swings from its maximum positive voltage, to the maximum negative voltage, as fast as it can, something that you will never use when driving speakers with audio (Unless you want to blow up your tweeters)
however, as amps use the output devices in linear mode, they disappate heat - allow for 50% efficiancy generally, perhaps less in a car amp since it has a switchmode voltage step up to waste more energy, so your (30 by 2) 60 watts of audio is actually 120 watts in from the power supply, with about 60 watts of heat into your cabinet, crude maths, but likly close enough to get you there.
In addition, the 300 watt car amp is most likly measured at 14.8 volts, which is the maximum charging voltage you will see in a car when its either really cold or really hot (Cant remember which) - and you are only giving it 12 volts, so the power output will not be near what they claim.
Anyway, the PC PSU _should_ have overload protection, and overheat protection, so if the amp does start to suck the juice too much, the PSU should shut down, but no guarentes naturally.
Perhaps put a blade fuse inline to the amp thats one step below the max 12 output of the PSU?