Hi, thought I'd pay it forward and share how I fixed my 07 Monte Carlo plastic glove box door where it detached from the metal hinge.

REPAIR STICKY:

SITUATION:
Problem is the door's plastic hollow posts are melted into the metal hinge for attachment, instead of using screws, so it's a weak design.

Also when the box is fully opened, held by the right retaining strap, the left side stop tab is not yet touching, so this causes a twisting to the door which aggravates the weak door attachment design.
See, the box on the left side looks to be missing a supporting retaining strap but it's not. Because on this model chevy, even though there's a hole, Chevy is relying on the stop tab on that side.
On sibling models such as the Impala that also have a left side strap, it is a spring loaded string which the Monte Carlo does not seem to have a mounting for the spring up above.
The fix for the left stop not touching/supporting is to add a thick rubber bump piece glued on to the flat plastic stop surface. Now the door will no longer be under a twisting force.
If your door hinges hasn't broken off yet, adding this might keep it from ever happening.

Mine just fell right out off of the hinge, breaking the thin melted plastic attaching enlarged squash heads.

The fix I did is very solid and successful although it takes some patience and 4 to 8 to properly size screws:

ITEMS NEEDED:

1. Up to 8 small screws(although 4 is probably enough to make the good enough repair).
2. Phillips head screw driver.
3. Cigarettes lighter.
4. Small socket(don't remember size..5/16" or) to remove the metal hinge from vehicle.

PROCEDURE:

1. Empty the glove box bucket of personal contents.
2. Remove the door's attached box/bucket from the plastic door by removing its 4 screws using the Phillips head screw driver to gain full access to the door's hinge attachment area.
3. Removing the bucket will allow you to just leave the bucket hanging in place and it's side strap stop attached to it and the vehicle. So no need to detach.
   1. Note which hinge surface attaches to the door and the way it attaches so you can reattach it correctly during the repair.
   2. Note the hinge design is actually fully open when the door is closed to eliminate reinstallation confusion.
4. Remove the metal hinge from the vehicle using a socket to remove the attaching hex screws.
5. You can leave any remnants of the melted plastic posts in the metal hinge holes. They will not make a difference to the addition of the new screws.
6. Sitting at a newspaper covered table, and a collection of screws, find up to 8 small short screws to use for the repair, which are very similar or identical to the 4 screws that attach the bucket.
7. Screws that are just the right size to fit, without breaking plastic, with some heat to tap the plastic holes, to screw into the rigid plastic posts.
8. Screws also must be short (especially for the shorter posts).
9. Notice the door has 3 plastic unmelted hallow posts for positioning the hinge plate. These unmelted hollow pins will be left unaltered in the repair, however you can use them to see if your repair screws appear to be the right diameter to just grip the plastic hole.
10. Just use your fingers and a hand screw driver to try to screw a few threads into the hole without any heat.
11. i.e. If the screw is way too tight, then your 8 screws' diameter is too big/thick, use smaller. If the screw doesn't contact the hole at all, use thicker screws.
12. The plastic is thin, you must use the proper size screws for this project for success. Look at the 4 screws that hold the bucket, sized something like these are ideal.
13. Dash screws are often this size if you can procure some from a salvage yard vehicle.
14. Place the metal hinge plate in the correct position onto the door.
15. Now with the correct size screws, gingerly hold one by its screw head between your fingers.
    1. While holding, use the flame from a cig lighter, to heat the tip of the screw JUST till/when the head is too hot to hold (you may want to wear a glove to insulate the heat a bit if you have sensitive fingers).
    2. Because if you don't heat the screw before insertion and screw slowly, it will not soften and tap the plastic hole but instead crack the thin plastic post.... Then you'll have to try to super glue baking soda repair the post back on... to try again.
16. Now take the hot tipped screw and using a manual or electric screw driver, begin to Slowly screw it into the hollow center of one of the 8 OEM melted top posts.
    1. If using an electric screw driver-set it on low slow speed and low torque settings.
    2. Screwing through the OEM melted top of the post can be a small challenge, to get through to the hallow center, but work patiently.
    3. Either a pointed tip or self taping tipped screw may go in easier, taping the hole.
17. As you go with your first screw, look under the hinge at the post to make sure the screw isn't too big, causing the post to expand or crack.
18. If the screw gets too tight going in, then the screw diameter might be too thick or the screw tip may need reheating(just unscrew and reheat the tip).
19. When the screw head makes contact and tightens, that screw is done.
20. Reinstall the door to the vehicle, by reinstalling the hinge hex screws.
21. Reinstall/attach the hanging in place bucket to the door with the 4 OEM screws. Situate the bucket so its stop is inside the dash opening, otherwise squeeze the bucket so it's stop clears the dash so it can swing all the way closed.
22. Trigger the door open latch handle to make sure its mouth is in the open position before closing the door, in case it got bumped closed.
23. Also this site has great views of all this common glove box components, positions and you can see if your door might be missing a retaining strap which aggravated the hinge breaking in the first place:

https://www.ifixit.com/Guide/2000+20...+Removal/90485

PICTURE:
Here is the door and bucket installed with the hinge attached with the new 8 screws: