I don't know how many times I repeat this over and over again in my singing lessons, I'm beginning to sound like a broken record.You could easily get away with mumbling your way in speech...with your mouth half closed, but when it comes to singing you're not going to get very far. You have to drop the jaw, take your voice back to the voice box, and use the vocal chords. Open your mouth to sing. There are no shortcuts. If you want to sing, I'm afraid, you will have to open your mouth. In order for that sound to come out loud and clear (and for you to hit the high notes with ease), you'll want a nice open throat. Try singing the vowels "A E I O U" with a half open mouth; and then place two fingers between your teeth to create a gap, and then go back to sing the vowels whilst maintaining that amount of space between your teeth. Look in the mirror as you do this. Chances are - if you do this correctly, you will hear a completely different (and better) sound in the latter.
For a detailed explanation on vocal cords, go to this article on Wikipedia