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First, did you really intend to type 2000 watt amplifier??
If base amp really put out that kind of power, I would expect that it would blow all the windows out of your car. Just for the sake of instruction however, lets assume that it does.
Each time the amp peaks, it is drawing something on the order of:
2000 watts/12 volts = 167 Amps
That's more than your car requires to start. Unless the electrical cable from your battery to the amp is as thick as the cable to the starter, and equipped with a starter-sized relay, I think we can agree on why you may be smelling burning wires.
Even a police alternator will not put out 167 amps for an extended period without overheating, and it will only do it at cruising RPM, not at idle. Your stock alternator will only do a third of that.
Assuming that you have heavy enough wires, when your starter draws that kind of power, you battery may dip to around 10 volts (lower if the battery is not big enough or in good shape). If your wires are not heavy enough, they heat up, increasing resistance, so you see further voltage drops across the wires. I'm guessing that even if your amp is only 200 watts, if you put a voltmeter across the power leads while running your stereo, you won't see the required 12.6 volts when you crank it up. When the voltage drops to a certain point, it will cut out.
Drawing down your system voltage at idle will also make your spark weak, causing your car to die at idle.
Bottom line, get a voltmeter and start checking system voltage at the amp and work back all the way to the battery until you find where the voltage loss is. You may even find that it is corroded battery cable clamps.
Speaking for all the other middle-aged bricksters (who I notice declined to respond to your question) if it really is a 2000 watt amp, don't do anything. With luck, perhaps it will catch fire before the next time it pulls up next to us at a stoplight. :)
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