Under-powering LED's

I have a 180 watt bank of LED lights but only have a 70 watt power supply, would using them together damage either one? Will the lights just be dimmer or will the ps heat up? I have a ps coming that is more than adequate but need to use the lights in the mean time and don't want to cause any damage.
Thanks for your help!

LEDs are fine with low voltage / current. Power supply may suffer..

would using them together damage either one?

Yes the power supply would be damaged unless you limit the current through the LEDs with appropriately valued resistors.
Normally for a high current LED you need a constant current supply not a resistor, but winding the power down you could probably get away with a resistor.

I've got a spare computer atx power supply somewhere, maybe I'll use it for the time being. If I connect all of the 12v wires together it should be sufficient to carry 15 amps, shouldn't it? I believe it's a 400 watt ps but that is distributed somehow through the 3.3/5/12 volt outputs isn't it?

Also - would the power supply be in danger of overheating and either shorting or catching fire or would it just die an agonizing death? Unless it would be a hazard I may just use it and take my chances, it's only for a few hours this weekend that I need to have it working.

Some power supplies will just shut down others will get very hot and catch fire. You just can't tell.

You seem quite lax with voltage figures, as if you're only running on watt figures.