It's never a good idea to driver speakers with an amp that isn't designed for the load. If your amp or receiver is intended for 6 or 8 ohm speakers, a lower impedance can cause problems.
If you do connect speakers with a lower than recommended impedance, your amp will probably not blow up immediately. Consider this a temporary pairing at best and if you insist on an imcompatible pairing, you will need to take some precautions as outlined below.
The reasons behind limits
When speakers are connected to an amplifier, those with a lower impedance present a greater challenge. The lower the impedance, the higher the current and power output. Dedicated power amps have a relatively simple task and are normally able to handle a 4 ohm load which is adequate for almost any speaker. AV receivers cram a great deal more into one box and also have 5 - 7 channels or more. The most popular budget to mid level receivers are bound by economical restraints and so are forced to cut some corners on the most expensive parts - the heatsink, transformer and the case itself. The result is the power supply is not able to supply the extra power demands that come with a lower impedance. Typically with a 4 ohm load the amp would output 50% more power. Downsizing the power supply means the amp will run out of power and the amp will clip. The rest of the amp is then designed for either a 6 or 8 ohm load which is less demanding. Downsizing the heatsink means that the output devices will heat up quicker if driven hard for an extended period.
In a nutshell, features sell AV receivers. The hidden parts that make an amp stable into 4 ohm loads are much less impressive, hence it is only higher end units that can drive such a load.
What happens if you push the limits
If you push an amp, two things can happen. The first is that it will reach it's limit and then run into clipping. At this point, the sound quality takes a hit and there is the risk of damaging the tweeters. The highest risk occurs with music where the level is continuous. Movies present a lesser risk because of the greater typical dynamic range. The second thing that can happen is that the amplifier overheats and goes into thermal shutdown. If this happens, you haven't damaged your amplifier yet, but you are shortening it's life and can expect it to fail if you don't make some changes.
There are two basic ways to avoid having problems:
1. Control the volume sensibly - you will need to reduce it significantly.
2. Avoid the build up of heat
Firstly, the amp should not be placed into a closed rack and if this can't be avoided, fans should be installed that come on automatically (without fail) when the system is in use. Ideally recommended clearances around the amp on all sides should be followed, perhaps to a higher standard than found in the manual. Avoid sources of heat. Never place another component on top or block ventilation openings.
1. More efficient speakers
Speakers with higher efficiency require much less power. Commercial options like Seaton Sound and JTR offer value for money solutions. DIY solutions such as the Econowave speaker are also viable alternatives.
2. Dedicated power amplifiers
Dedicated power amps will handle 4 ohm loads with ease as this is the task they are designed for. Affordable options include Behringer A500 which is a studio amp with 230w into 4 ohms. For a little more, the Alesis RA500 can do a similar job. Emotiva also offer very good value for money multi channel power amps which make most receivers look like toys.