Two issues here:
1) product
2) acoustics
There are challenges with both -
You need a speaker that has the excursion capability to play that low (the lower you play a speaker, the greater the excursion it needs to reach - increases on the order of 2x per octave). When you reach the excursion limits of the speaker, that's all she wrote... you can't turn the volume up louder.
So... you might be compromising overall loudness with this approach - and that's one big reason it's not done. Even "hardcore SQ competition systems" that DO extend this low aren't designed to play at real 'rock out!' volume levels.
It's also one reason subwoofers have such significantly higher excursion capabilities than midranges do.
Higher end Focal component sets have remarkably high excursion capabilities - but even those, I'd be concerned running down to 50hz. Look at the Polyglass and K2Power if you are interested, but it's out of your budget.
I'd suggest purchasing a more "pedestrian" component set, something that delivers sonics that you know you like (chosen with YOUR ears). Hey, buy a nice little 4" set. Put the 4" in the kickpanel.
And then augment that, turn it into a 3-way by putting two of these 6.5"
subwoofers in your doors:
http://www.partsexpress.com/pe/pshowdet ... er=264-832
NO 6.5" touches that excursion. It also has a low FS to actually extend low - something a 2-way component set can't afford to do. And the motor is designed to have that excursion - something that would sacrifice speed in a driver meant to play up into the midrange.
That's the equipment side of things...
...realistically, speakers need cabinets - particularly bass speakers.
If the sound energy from the rear of the cone can escape the door cavity, it'll cancel the sound energy from the front of the cone.
Well - it gets worse as the frequencies get lower. In fact, with short wavelengths you wouldn't even necessarily hear much degradation of the high frequency component of the sound - but the symptoms with ANY system suffering this is, simply, poor bass response from the front speakers.
If you pop your door panels off, you'll see the problem - open holes leading into the inside of the door cavity.
That's no "speaker cabinet"!
I generally use damping material - the heavy stuff with the aluminum backing - one layer inside the door cavity (inside of the outer door skin), and then one layer over the inner door structure - including multiple layers to bridge over those holes - creating a pseudo-rigid structure, and making a more optimal enclosure out of your door.
That's the only way to get bass from your front speakers - you could mount a 10" subwoofer in the door, and by virtue of acoustics, cancellation would prevent it from making bass, unless you took measures like this.