basic and some times forgotten trick to stiffen break peddle. in park with car off pump breaks until there rock hard to press, start car pump one or two more times turn off car and repeat. works well with all cars ive owned (newest model year is 2006 ) it is best done after bleeding to get the strongest and stiffest peddle.
Ok...so when you replaced that caliper did you open the bleeder and let gravity remove air from it before you started bleeding your brakes? I'd guess the problem is with that caliper and it still has air in it, normally when you replace a caliper you would install it and make sure the master cylinder is topped off (leave the lid off the master cylinder) , then open the bleeder and let gravity push air out of the caliper, then when you have brake fluid coming out of the bleeder you would close the bleeder and begin the bleeding process.
Thing is if you let the master cylinder go dry while you had the hose disconnected replacing the caliper you have air from the master cylinder to the caliper in that line which would account for the issue your having, if you didn't notice that the master cylinder was empty and started bleeding the brakes then you would have air trapped in the master cylinder and possibly the line running to the other caliper also.
Anyway if only one portion of the master cylinder went dry ( the other chamber still had fluid in it ) then the front is the only thing you need to rebleed you do not need to do the rear brakes unless both chambers in the master cylinder went dry.
I'm going to bet that you have air in the side you replace the caliper on that you haven't gotten out yet which is causing your spongy pedal., interesting that your '07 Cobalt doesn't have ABS that seems very odd to me, but hey anything is possible.
(edit) Just for safety sake if you by chance do have ABS and you have air trapped between the master cylinder and the ABS unit then I can tell you a way to maybe purge it out at least to the caliper where you can bleed it out normally, what you need to do is find a gravel parking lot or road where you can safety get up to say 30 mph then cram on the brakes making the ABS activate (only will work on gravel because you need the wheels to lock and the ABS pump to run) once it activates (do this a couple times) you should be able to bleed the air out through normal bleeding like you' ave been doing, if the car truly doesn't have ABS then just disregard what I'm telling you.
To find out if you have ABS follow the brake line coming from the master cylinder if the front lines run directly to the caliper (or a proportioning valve (small semi-flat with lines going in and out ) then you don't have ABS, but if the lines run to a rather large box with a motor and a bunch of brake lines then you do have ABS.
The ABS unit for your car would look something like this.
The proportioning valve will look like this...
I did some research and ABS seemed to be an extra for the two base models and the two higher end models had it as a standard feature.
yeah....it's odd to see a GM car these days with out ABS, but it happens.
Here is the correct way to bleed brakes - you will NEED two people.
Do all the following with the engine OFF
To start off, jack up the car, place axle stands at all corners and remove all wheels. Never get under a car held up by just a jack.
1. Remove the master cylinder dust cap and using a syringe remove all the brake fluid in the reservoir.
2. Fill the reservoir with new brake fluid - make sure it is the right type of brake fluid. Not all types are compatible with every car.
3. Leave the cap off the master cylinder reservoir and get person 1 to sit in the drivers seat.
4. Person two should go to the first brake to be bled - which ALWAYS should be the wheel closest to the master cylinder.
5. Person 1 pumps up the brake pedal until hard, then waits with pressure HELD ON THE PEDAL
6. Person two will need a 10mm (usually) spanner and either a brake bleeder bottle or a piece of vacuum tube.
7. P2 should crack the bleeder valve then place the vacuum tube on the nipple and make sure it stays in such a way that the end of the vacuum tube is ALWAYS higher than the brake caliper.
8. As P2 opens the bleeder nipple just enough to let fluid out slowly, P1 should depress the brake pedal almost all the way to the floor. At this point P1 MUST NOT LET THE PEDAL BACK UP AT ALL.
9. When the pedal has been depressed P2 should close the bleeder nipple and then let P1 pump up the pedal again.
10. Repeat unitl either there are no more air bubbles coming out of the bleeder nipple - or unitl the new fluid comes out (this is preferable, and is required if doing a brake flush).
11. After each few bleeds check the fluid level in the brake cylinder and top up if necessary.
12. Repeat above steps going around the vehicle in such a way that the longest brake line is done last.
13. Fill brake reservoir to indicated level, clean dust cap and cover reservoir.
NEVER reuse brake cylinders on drum brakes - always replace them with every new set of brake shoes.
DONT top up brake fluid in between brake flushes - the lower the brake fluid level - the less brake pad you have left (or you have a brake fluid leak somewhere)
If your vehicle says to use DOT 3 - this is a MINIMUM - BUT if you want to use a higher grade of fluid make sure it is compatible with your car!
ALWAYS replace your brake fluid - full system bleed - every 2 years AT THE MOST - Brake fluid is mostly glycol-ether based but some like Citroen/Rolls Royce use Mineral oil, and DOT 5 is silicone based (hence the point above) Brake fluid also absorbs moisture from the air - this is why it must be replaced after a year or two. The more moisture in the fluid, the more likely you will suffer from soft brake pedal due to compress-ability.
NEVER get brake fluid on your paint - it will dissolve it like paint stripper but slower.
This might sound complicated but its really easy and should only take 15 - 30 mins to bleed an entire car and replace all fluid.
Just solved a spongy brake problem with my car a couple weeks ago. I changed the brakes, and bled the fluid, and still it was spongy. I had my GF look under the car while I pressed on the brake and boom... We found a leak.
But that's my scenario. Yours is probably not leaking, just needs a proper bleeding. There's probably some air stuck in there. Just make sure you use fresh brake fluid, and bleed it properly.
I've tried this a few times, using basically the same procedure with brand new DOT 3 fluid.. but i went in the order of RR, LF, LR, RF because that is what is recommended by chevy for my car. But, I guess I could try it again
Only one chamber to the master cylinder, and ya my car is the very base model of a very cheap car so no abs.. and no auto locks/windows on an 07.. very surprising :p, but I did not gravity bleed them at all, I think I might do that next weekend and see how it goes!
I will try this tomorrow morning and see if this helps at all.. Thank you!