You should not use that driver if you think you'll be pulling that much current. For one, it's rated for 3A for a maximum of 10ms per the datasheet and you'll certainly try to draw for longer than 10ms in a stalled condition. And that is the maximum rating for the device which the datasheet says is not to be exceeded under any circumstance. It sounds to me like you'll be abusing the poor thing. Find a beefier driver, or if you're feeling really adventurous, parallel two of them. Is that a good idea? I've never done it, never heard of it being done, and wouldn't do it myself, but you could certainly try :)
I would just find another motor driver on pololu's site. It looks like there's plenty of them. Make sure their maximum CONTINUOUS current is greater than your stall current.
My answer assumes you are using a permanent magnet DC motor (i.e. permanet magnets form the stator, the armature is wound with copper wire in a multi-pole arrangement, and current is passed to the armature coils thru brushes). My answer would be similar for a brushless DC motor.
As others have indicated the danger in running the motor at high current is the production of heat by the resistance of the armature coils. That's good old I-squared-R heat, measured in Watts. This heat production causes an increase in temperature of the armature coils and the iron structure of the armature. Some of the heat is transfered to the stator and the case of the motor, but efficient transfer is thwarted by the inherent air gap separating the outer armature surface from the innere stator surface. This characteristic of the motor works to confine the I2R heat in the armature and cause its temperature to rise dramatically faster than that of the stator or the case. So, meauring the case temperature gives only a hint at the temperatures which are actually being experienced inside the armature while the motor is being run at the high current you are concerned about.
Eventually, these high temperatures will break down the enameal insulation of the copper magnet wire in the armature causing inter-turn shorts. These shorts in turn prevent current from flowing in sections of the armature coils, which in turn reduces the magnetic field produced by the armature, which in turn reduces the torque produced by the motor. The symptom you will sooner or later notice is that the motor tends to get weaker with use or "age". More and more armature coils are shorting, weakening the motor incrementally with each new occurance.
The other prominent malady of extended overheating is that the solder used to connect the various armature coils to the commutator will melt and fly away from the solder joints by centrifugal force of the rotating armature. The solder employed for this task is usually a high temperature variety for exactly this reason. Still, everything has its limits! Eventually, the motor will lose connection to one pole, then another, etc. The symptom is that the motor will stall at slow speeds, or not start at all in certain shaft positions. This is because the motor has no torque in these positions because the armature is open circuited. Twist the shaft a little and the motor will start and have enough inertia to "run over" the dead spot in the armature if the shaft load is not to great.
Yet another symptom of extended overheating is that the armature shaft, or the armature itself, will warp from the high temperatures and bind with the stator. The "binding" may only be partial and the armature will rub against the stator wearing away metal on both surfaces in the process. Or, the warp will become bad enough, quick enough that the two surface will simply crunch together, perhaps creating a "weld" in the process. The warped armature symptom is usually accompanied by a certain amount of noise - maybe the really cool noises you are trying to exploit in your project!
There are various tests that can be performed to evaluate the amount of heating created in the armature in an effort to determine how likely the motor is to succumb to one of the three maladies described above. However, they are all pretty complicated, requiring disassembly and reassembly of the motor as well as armature modifications.
Perhaps the best way to test in a situation like yours is to make a "dynamic brake" which will load your motor to the torque and current levels you intend to use in the application. Make the dynamic brake from another permanent magnet motor, preferably a larger one. Couple the two shafts firmly together and mount the motors rigidly. Next, connect a high wattage resistor to the larger dynamic brake motor's supply leads (do not power this dynamic brake motor from a pwoer supply, simply attach the resistor to its leads). Next drive your test motor from the same voltage you are using in the application and monitor its current with a low-resistance ammeter. Now, adjust the load resistor attached to the dynamic brake motor until you get the same current you expect in your application ( "50% +" amps as you stated in your question). The load resistor must be a high wattage type because it will make quite a bit of heat. You can use multiple values in series and parallel to achieve the desired value. Or, you can use a suitably sized rheostat ( not a potentiometer!).
Once you have all this running and you are monitoring the current being drawn by your test motor with the ammeter, simply wait and observe for one of the above symptoms ( or another I haven't predicted) to occur. Keep an eye on that ammeter because it will show you the onset of failure symptoms. The current can either rise, fall, or flucuate sproadically depending on the failure mode. If the motor runs flawlessly for X times longer than you intend to use it in your application, you are probably OK long term operation. (X = 5 to 10 ).
By the way, the "dynamic brake" DC Motor used in this test is actually being used as a generator, the energy produced by the test motor is being passed thru this generator and being dissipated in the external resistor. In the process the shaft of the test motor is experiencing a torque level identical to what it would in your target application. Remember, in a PM DC motor amps = torque ( simply stated).
Good Luck!!!
Best Answer
The L293B (or D) is really a limiting factor on this design. When used in a H bridge configuration from a 3.6 V supply, you'll be lucky to get more than 1.5 volts across the motor. This is because of the turn on saturation voltage in the driver transistors. Check out this data sheet and look for \$V_{CEsatH}\$ and \$V_{CEsatL}\$ on page 4 - they tell you that at 1 amp the top transistor saturation voltage is typically 1.4 volts an the bottom transistor saturation voltage is typically 1.2 volts.
Upshot of this is that you can probably use a much smaller motor for the steering if you used a better driver. See this for a more complete explanation.
Using a better driver will also improve traction, power and efficiency on the rear drive motor too.
Another option for the steering is to use a servomotor - this can be positioned to just avoid mechanical end-stopping and therefore reduce current consumption.